
HELLAL Abdelaziz
هلال عبدالعزيز
abdelaziz.hellal@univ-msila.dz
06 65 95 96 24
- Mathematics Department
- Faculty of Mathematics and Informatics
- Grade MCB
About Me
Doctor of Science. in Higher Normal School of Kouba, Algeria
Research Domains
Functional Analysis for Partial Differential Equations
LocationMsila, Msila
Msila, ALGERIA
Code RFIDE- 2023
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Encaderement master
Naidji Ali
Some Existence and Regularity Results for Unilateral Problems with Degenerate Coercivity
- 2023
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Encaderement master
Zerrouki Fouzia
On Weak Lebesgue ( Marcinkiewicz ) Spaces with Variable Exponents
- 2023
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Encaderement master
Naidji Ali
Master memory beamer-Some Existence and Regularity Results for Unilateral Problems with Degenerate Coercivity
- 2021
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Encaderement master
Lakehal Hadjira
Some remarks to anisotropic variable exponent Sobolev spaces
- 2020
- 2020
- 2020
- 2019
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Encaderement master
Anouar Islam GHEHIOUECHE
On Lebesgue and Sobolev Spaces with Variable Exponents
- 2015
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Licence
Riyadh Saadallah , Bilal Ibrahimi
Study of Young's and Hölder's inequalities in L^p(·)(\Omega)
- 2015
- 2015
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Encaderement master
Ahmed Djouabi , Mohamed Mihoubi
Study of Poincaré's inequalities in L^p(·)(\Omega)
- 01-10-2024
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Doctor of Science
ANISOTROPIC ELLIPTIC AND PARABOLIC EQUATIONS WITH VARIABLE EXPONENTS AND L1 DATA - 04-01-2012
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Magister degree
On study of the Lewy-Stampacchia's inequality by a penalization method - 28-06-2006
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PES Diploma in Mathematics
Sequences and Their Applications - 10-07-2001
- 05-07-2001
- 1980-11-06 00:00:00
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HELLAL Abdelaziz birthday
- 2025-02-22
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2025-02-22
Neumann boundary value problems in anisotropic Sobolev spaces with variable exponents
In work, we demonstrate a trace theorem that facilitates the handling of Neumann problems with nonlinear boundary terms in anisotropic spaces characterized by variable exponents. Following this, we explore a problem involving generalized p(⋅)-Laplacian-type operators. We establish the existence of solutions and pay particular attention to cases where the solution is unique.
Citation
Hellal ABDELAZIZ , ,(2025-02-22), Neumann boundary value problems in anisotropic Sobolev spaces with variable exponents,The 1st National Colloquium on Mathematics: Trends and Actual Applications (CNMT2A),The Faculty of Sciences of the University of Algiers 1
- 2025-02-02
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2025-02-02
Regularity results for a singular elliptic equation involving variable exponents
In this paper, we investigate the existence and regularity of nonnegative weak solutions for specific class of nonlinear singular anisotropic elliptic problems with degenerate coercivity involving variable exponents. We show that certain lower-order term contribute to the regularization of solutions, as well as the regularization induced by a singular nonlinearity term. Our methodology employs an approximation technique that integrates anisotropic variable exponent Sobolev spaces, truncation methods, compactness arguments, and Schauder’s fixed-point theorem. These findings extend some previous results established under constant exponents.
Citation
Hellal ABDELAZIZ , Rabah Mecheter , , (2025-02-02), Regularity results for a singular elliptic equation involving variable exponents, Boletim da Sociedade Paranaense de Matemática, Vol:43, Issue:3, pages:25, Sociedade Paranaense de Matemática
- 2024-12-25
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2024-12-25
Double phase problems with variable exponents
This work examines a class of double-phase elliptic problems involving variable exponents and irregular data. Under carefully chosen assumptions on the data, we apply the compactness method to prove the existence of weak solutions to the problem. Moreover, we explore the regularizing effect introduced by the additional term, which enhances the summability properties of the solution for the double-phase problem being studied. Our analysis provides deeper insights into the interplay between the structure of the problem and the regularity of its solutions.
Citation
Hellal ABDELAZIZ , ,(2024-12-25), Double phase problems with variable exponents,International Conference on Mathematics and its Applications in Science and Technology (ICMAST'2024).,Setif 1 University Ferhat Abbas Setif; Algeria
- 2024-12-04
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2024-12-04
Certificate of recognition
I am pleased to acknowledge that I was awarded a Certificate of Recognition for my contribution to the National Conference on Mathematical Analysis organized by the University of M'sila.
Citation
Hellal ABDELAZIZ , ,(2024-12-04), Certificate of recognition,National Conference on Mathematical Analysis (NCMA-2024),University of M'sila, Faculty of Mathematics and Computer Science
- 2024-11-28
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2024-11-28
Regularizing effects in some anisotropic nonlinear dirichlet problem
This work investigates the regularizing effects in a class of anisotropic nonlinear Dirichlet problems. We consider elliptic equations with anisotropic growth conditions, where the nonlinearity and the associated differential operator exhibit non-standard behavior influenced by directional dependencies. Under suitable assumptions on the structure of the problem, we establish the existence and uniqueness of weak solutions. Furthermore, we analyze the regularizing effects induced by the anisotropic nature of the problem, which lead to improved regularity and summability properties of the solutions. Our results highlight the interplay between the anisotropic structure and the smoothing mechanisms, providing a deeper understanding of how directional growth conditions influence the qualitative behavior of solutions. These findings extend existing theories and offer new insights into the analysis of anisotropic partial differential equations.
Citation
Hellal ABDELAZIZ , ,(2024-11-28), Regularizing effects in some anisotropic nonlinear dirichlet problem,Second National Conference on Mathematics and Applications,Mohamed Boudiaf University - M'sila - M'sila (Algérie)
- 2024-11-19
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2024-11-19
Existence of weak solutions to double phase problems with irregular data
This study focuses on a category of double-phase elliptic problems characterized by variable exponents and irregular data. By imposing appropriate conditions on the data, we utilize the compactness approach to demonstrate the existence of weak solutions to the problem. Furthermore, we emphasize the regularizing influence of the additional term on the summability properties of the solution for the double-phase problem under investigation.
Citation
Hellal ABDELAZIZ , ,(2024-11-19), Existence of weak solutions to double phase problems with irregular data,The 1st International Conference Mohand Moussaoui on Applied Mathematics and Modeling,Université 8 Mai 1945 Guelma
- 2024-10-23
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2024-10-23
Existence results for double phase problems
This presentation will focus on some existence results for double phase problems.
Citation
Hellal ABDELAZIZ , ,(2024-10-23), Existence results for double phase problems,8th M’sila Conference on Mathematical Analysis (8MCMA’2024),Faculty of Mathematics and Computer Science, University of M’sila
- 2024-10-23
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2024-10-23
Certificate of Appreciation
Certificate of Appreciation
Citation
Hellal ABDELAZIZ , ,(2024-10-23), Certificate of Appreciation,8th M'sila Conference on Mathematical Analysis (8MCMA2024),Faculty of Mathematics and Computer Science-University of M’sila
- 2024-06-26
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2024-06-26
Some regularity of the solution to nonlinear singular anisotropic elliptic equations with variable exponents
The aim of this presentation is to study a Dirichlet problem characterized by degenerate coercivity, involving variable exponents and a singular nonlinearity
Citation
Hellal ABDELAZIZ , ,(2024-06-26), Some regularity of the solution to nonlinear singular anisotropic elliptic equations with variable exponents,National Conference: Mathematical Modeling for Dynamic Systems (M2DS’24),Constantine, ALGERIA
- 2024-05-15
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2024-05-15
Singular Elliptic Problems for some Anisotropic Operators with Variable Exponents
The main focus of this presentation is singular anisotropic degenerate elliptic equations with variable nonlinearities.
Citation
Hellal ABDELAZIZ , ,(2024-05-15), Singular Elliptic Problems for some Anisotropic Operators with Variable Exponents,First International Conference on Nonlinear Mathematical Analysis and Its Applications (IC-NMAA’24),Bordj Bou Arréridj - Algeria
- 2024-04-23
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2024-04-23
Functional Analysis via Pedagogical Days 24
The presentation was focused on How can I choose my specialty?
Citation
Hellal ABDELAZIZ , ,(2024-04-23), Functional Analysis via Pedagogical Days 24,Pedagogical Days 2024,Faculty of mathematics and computer science, University of Mohamed Boudiaf M'sila
- 2024-04-02
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2024-04-02
Some Formulas in Geometrical Method
Science, Technology, Engineering, and Mathematics, considered as a group of academic or career fields (often used attributively). We are interested in the challenges and the perspectives of teaching STEM in the technical classroom, so what are challenges and perspectives of teaching STEM in the technical classroom? The aim of this presentation is how to explain and clarify some formulas via geometrical method using some technical classroom. N.B. We refer the link: https://www.mathdoubts.com/a-plus-b-whole-square-geometric-proof/
Citation
Hellal ABDELAZIZ , ,(2024-04-02), Some Formulas in Geometrical Method,Teaching STEM in the Technical Classroom : Challenges and Perspectives,University of El Oued, Algeria
- 2023-12-30
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2023-12-30
Singular Elliptic Equations with Variable Exponents
Abdelaziz, H. (2023). Singular Elliptic Equations with Variable Exponents. International Journal of Mathematics And Its Applications, 11(4), 141–168. Retrieved from https://ijmaa.in/index.php/ijmaa/article/view/1440
Citation
Hellal ABDELAZIZ , , (2023-12-30), Singular Elliptic Equations with Variable Exponents, International Journal of Mathematics And Its Applications, Vol:11, Issue:4, pages:28, https://ijmaa.in/index.php/ijmaa/article/view/1440
- 2023
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2023
On Anisotropic Degenerate Parabolic Problem with Variable Exponents
In our work, we present the prove of the existence and the regularity of weak solutions for a class of nonlinear anisotropic parabolic equations with pi(·) growth conditions, degenerate coercivity and Lm(·) data, with m(·) > 1 being small. The functional setting involves Lebesgue-Sobolev spaces with variable exponents.
Citation
Hellal ABDELAZIZ , ,(2023), On Anisotropic Degenerate Parabolic Problem with Variable Exponents,International Conference of Young Mathematicians,Institute of Mathematics of NAS of Ukraine. Kyiv, Ukraine.
- 2023
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2023
Parabolic problems for some anisotropic operators involving variable exponents
The main point of this presentation is studying the existence and regularity of solutions for some nonlinear parabolic equations with a principal part characterised by degenerate coercivity involving varaible exponents.
Citation
Hellal ABDELAZIZ , ,(2023), Parabolic problems for some anisotropic operators involving variable exponents,2nd International Conference on the Evolution of Contemporary Mathematics and their Impact in Sciences and Technology,Mentouri Brothers University of Constantine
- 2023
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2023
Certificate of Appreciation
National Seminar Mathematics, Mathematics and Society (MMS 2023) University of M’sila and ENS Bousaada October 25-26, 2023
Citation
Hellal ABDELAZIZ , ,(2023), Certificate of Appreciation,National Seminar, Mathematics, Mathematics and Society (MMS 2023),University of M’sila and ENS Bousaada
- 2022-05-16
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2022-05-16
Anisotropic Parabolic p-Laplacian Equations
In this work we prove the existence and uniqueness of both entropy solutions and renormalized solutions for an anisotropic parabolic p-Laplacian equations with $p_i$-growth conditions using the penalization method. Moreover, we obtain that entropy solutions coincide with the renormalized solutions.
Citation
Hellal ABDELAZIZ , ,(2022-05-16), Anisotropic Parabolic p-Laplacian Equations,Journée Scientifique des Mathématiques et de I'Informatique (JSMI2022),Djilali Bounaâma Khemis Milliana University
- 2022-04-25
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2022-04-25
Nonlinear anisotropic degenerate parabolic equations with variable exponents and irregular data
In this paper, we prove the existence and the regularity of weak solutions for a class of nonlinear anisotropic parabolic equations with pi( ⋅ ) growth conditions, degenerate coercivity and L^m( ⋅ ) data, with m( ⋅ ) > 1 being small. The functional setting involves Lebesgue-Sobolev spaces with variable exponents.
Citation
Hellal ABDELAZIZ , , (2022-04-25), Nonlinear anisotropic degenerate parabolic equations with variable exponents and irregular data, Journal of Elliptic and Parabolic Equations, Vol:8, Issue:1, pages:20, Springer
- 2022-01-01
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2022-01-01
Regularity of Weak Solutions to Elliptic Problem with Irregular Data
This paper is concerned with the study of the nonlinear elliptic equations in a bounded subset Ω ⊂ R^N Au = f, where A is an operator of Leray-Lions type acted from the space W^{1,p(·)}_{0}(Ω) into its dual. when the second term f belongs to L^m(·), with m(·) > 1 being small. we prove existence and regularity of weak solutions for this class of problems p(x)-growth conditions. The functional framework involves Sobolev spaces with variable exponents as well as Lebesgue spaces with variable exponents.
Citation
Hellal ABDELAZIZ , , (2022-01-01), Regularity of Weak Solutions to Elliptic Problem with Irregular Data, Mathematical Methods in the Applied Sciences, Vol:0, Issue:0, pages:9, Authorea
- 2022
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2022
On Anisotropic Parabolic Equations with Variable Nonlinearity
In this poster, we show you how to prove the existence and the regularity of weak solutions for a class of nonlinear anisotropic parabolic equations with p i (·) growth conditions, degenerate coercivity and L^m(·)data, with m(·) > 1 being small. The functional setting involves Lebesgue-Sobolev spaces with variable exponents.
Citation
Hellal ABDELAZIZ , ADMIN Admin , ,(2022), On Anisotropic Parabolic Equations with Variable Nonlinearity,Rencontre d’Analyse Mathématiqueet ses Applications (RAMA),Université de M’Sila
- 2022
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2022
Certificate of Recognition
I contributed greatly to success the 7th M’sila Conference on Mathematical Analysis (7th MCMA 2022) as a Member of the organizing committee.
Citation
Hellal ABDELAZIZ , ,(2022), Certificate of Recognition,7th M’sila Conference on Mathematical Analysis,M'sila
- 2022
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2022
Some Regularity Results for a Singular Elliptic Equations with Variable Exponents
This paper is concerned with study of the nonlinear singular elliptic equations in a bounded domain $\Omega\subset\mathbb{R}^N$, $(N\geq 2)$ with Lipschitz boundary $\partial\Omega$, $$ -\mathrm{div}\left(\widehat{a}(\cdot,Du)\right)=\frac{f}{u^{\gamma(\cdot)}}, $$ Where $f$ is a nonnegative function belonging to the Lebesgue space with variable exponents $L^{m(\cdot)}(\Omega)$, with $m(\cdot)$ being small (or $L^{1}(\Omega)$), while $m:\overline{\Omega}\to (1,+\infty)$, $\gamma:\overline{\Omega}\to (0,1)$ are continuous functions satisfying certain conditions depend on $p(\cdot)$. We prove the existence, uniqueness and regularity of nonnegative weak solutions for this class of problems with $p(\cdot)$-growth condition. The functional framework involves Sobolev spaces with variable exponents as well as Lebesgue spaces with variable exponents. Our results canbe seen as a generalization of some results given in the constant exponents case.
Citation
Hellal ABDELAZIZ , ,(2022), Some Regularity Results for a Singular Elliptic Equations with Variable Exponents,6th M'SILA Conference on Mathematical Analysis,M'Sila
- 2022
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2022
Renormalized and entropy solutions for nonlinear parabolic equations with L^1 data
In this work we prove the existence and uniqueness of both entropy solutions and renormalized solutions for an anisotropic parabolic $\overrightarrow{p}$-Laplacian equations with $p_i$-growth conditions using the penalization method. Moreover, we obtain that entropy solutions coincide with the renormalized solutions.
Citation
Hellal ABDELAZIZ , ,(2022), Renormalized and entropy solutions for nonlinear parabolic equations with L^1 data,The Second National Conference on Mathematics and its Applications (2nd SNCMA 2022),University of Bordj Bou Arreridj, Algeria
- 2021
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2021
Weak Solutions for the p(x)-Laplacian Equation with Variable Exponents and Irregular Data
In this work, we prove existence and regularity of weak solutions for a class of p(·)-Laplacian equations with variable exponents and L m data, with m being small. The functional setting involves Lebesgue-Sobolev spaces with variable exponents.
Citation
Hellal ABDELAZIZ , ,(2021), Weak Solutions for the p(x)-Laplacian Equation with Variable Exponents and Irregular Data,International Conference on Pure and Applied Mathematics. IC-PAM’21,Ouargla University, Algeria
- 2020
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2020
On solutions of nonlinear elliptic equations with variable exponents and irregular data
In this work, we prove existence and regularity of weak solutions for a class of p(x)-Laplacian equations with variable exponents and L^m data, with m being small. The functional setting involves Lebesgue−Sobolev spaces with variable exponents. The study of our problem in [4] is a new and interesting topic. Inspired by [1], [2] and [3] we prove the existence of weak solution for our problem with right-hand side in L^m and the variable exponent p(x) satisfies a condition of regularity. The main steps of the proof consist of obtaining uniform estimates for suitable approximate problems and then passing to the limit. [1] M. Bendahmane, P. Wittbold, Renormalized solutions for nonlinear elliptic equations with variable exponents and L^1− data, Nonlinear Analysis TMA 70(2), 567-583, (2009). [2] L. Boccardo, T. Gallouët, Nonlinear elliptic equations with right hand side measures, Comm. Partial Differential Equations 17, 641-655, (1992). [3] L. Diening, P. Harjulehto, P. Hasto, M. Rauzicka; Lebesgue and Sobolev Spaces with Variable Exponent, Book, Lectures Notes in Mathematics 2017. Springer-Verlang Berlin Heidelberg, (2011). [4] F. Mokhtari, K. Bachouche, H. Abdelaziz, Nonlinear elliptic equations with variable exponents and measure or L^m data. J. Math. Sci. 35, 73-101, (2015).
Citation
Hellal ABDELAZIZ , ,(2020), On solutions of nonlinear elliptic equations with variable exponents and irregular data,ICRAMCS 2020,Casablanca, Morocco
- 2019
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2019
ON p(·)-LAPLACIAN EQUATIONS WITH VARIABLE EXPONENTS AND L^m DATA
Abstract. In this work, we prove existence and regularity of weak solutions for a class of p(·)-Laplacian equations with variable exponents and L^m data, with m being small. The functionalsetting involves Lebesgue-Sobolev spaces with variable exponents.
Citation
Hellal ABDELAZIZ , ,(2019), ON p(·)-LAPLACIAN EQUATIONS WITH VARIABLE EXPONENTS AND L^m DATA,JAMA’19,Ziane Achour-Djelfa University
- 2018
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2018
Nonlinear elliptic equation with variable exponents and measure data
In this paper we prove existence and regularity of weak solutions for a class of nonlinear elliptic equations with variable exponents. The functional setting involves Lebesgue-Sobolev spaces with variable exponents.
Citation
Hellal ABDELAZIZ , ,(2018), Nonlinear elliptic equation with variable exponents and measure data,MATHEMATICAL DAYS V,M'sila
- 2015-10-08
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2015-10-08
NONLINEAR ELLIPTIC EQUATION WITH VARIABLE EXPONENTS AND MEASURE OR L^m DATA
In this work, we prove existence and regularity of weak solutions for a class of nonlinear elliptic equations with variable exponents and measure or L^m data, with m being small. The functional setting involves Lebesgue-Sobolev spaces with variable exponents.
Citation
Hellal ABDELAZIZ , kamel Bachouche, Fares Mokhtari, , (2015-10-08), NONLINEAR ELLIPTIC EQUATION WITH VARIABLE EXPONENTS AND MEASURE OR L^m DATA, Journal of Mathematical Sciences: Advances and Applications, Vol:35, Issue:10, pages:29, Scientific Advances Publishers : Available at http://scientificadvances.co.in
- 2011
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2011
SHS 2011
University of Sciences and Technology Houari Boumediene BP 32 EL ALIA, Bab Ezzouar, Algiers, 16111, Algeria
Citation
Hellal ABDELAZIZ , ,(2011), SHS 2011,The Second Seminar on the History of Sciences SHS 2011,University of Science and Technology Houari Boumediene, Bab-Ezzouar, Algiers, Algeria
- 2010
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2010
Our contribution without paper
Hellal Abdelaziz Attestation de participation Je soussigné, Abdelhafid Mokrane, Président du Comité d'Organisation des Premières Journées Scientifiques du Laboratoire Euro Maghrébin de Mathématiques et de leurs Interactions (LEM2I), a participé aux activités de ces Journées, qui se sont tenues du 13 au 22 juin 2010, au Centre Munatec de Tipaza, Algérie. certifie que Ministère de l'Enseignement Supérieur et de la Recherche Scientifique Ecole Normale Supérieure de Kouba – Alger ENS Kouba Premières Journées Scientifiques du Laboratoire Euro Maghrébin de Mathématiques et de leurs Interactions (LEM2I) 13-22 juin 2010, Tipaza, Algérie
Citation
Hellal ABDELAZIZ , ,(2010), Our contribution without paper,Premières Journées Scientifiques du LEM2I,MUNATEC, Tipaza, Algeria.