HELLAL Abdelaziz

Naidji Ali

Some Existence and Regularity Results for Unilateral Problems with Degenerate Coercivity

Zerrouki Fouzia

On Weak Lebesgue ( Marcinkiewicz ) Spaces with Variable Exponents

Naidji Ali

Master memory beamer-Some Existence and Regularity Results for Unilateral Problems with Degenerate Coercivity

Lakehal Hadjira

Some remarks to anisotropic variable exponent Sobolev spaces

Racha Bousbaa

On generalized Orlicz spaces

Racha BOUSBAA

On generalized Orlicz spaces_Master memory

Racha BOUSBAA

On generalized Orlicz spaces_Beamer

Anouar Islam GHEHIOUECHE

On Lebesgue and Sobolev Spaces with Variable Exponents

Riyadh Saadallah , Bilal Ibrahimi

Study of Young's and Hölder's inequalities in L^p(·)(\Omega)

Meriem Gana , Ibtissam Mekhfi

On the history of Variable Lebesgue Spaces

Ahmed Djouabi , Mohamed Mihoubi

Study of Poincaré's inequalities in L^p(·)(\Omega)

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.

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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

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.

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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

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.

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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

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.

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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

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.

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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)

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.

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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

This presentation will focus on some existence results for double phase problems.

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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

Certificate of Appreciation

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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

The aim of this presentation is to study a Dirichlet problem characterized by degenerate coercivity, involving variable exponents and a singular nonlinearity

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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

The main focus of this presentation is singular anisotropic degenerate elliptic equations with variable nonlinearities.

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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

The presentation was focused on How can I choose my specialty?

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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

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/

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Hellal ABDELAZIZ , ,(2024-04-02), Some Formulas in Geometrical Method,Teaching STEM in the Technical Classroom : Challenges and Perspectives,University of El Oued, Algeria

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

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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

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.

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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.

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.

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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

National Seminar Mathematics, Mathematics and Society (MMS 2023) University of M’sila and ENS Bousaada October 25-26, 2023

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Hellal ABDELAZIZ , ,(2023), Certificate of Appreciation,National Seminar, Mathematics, Mathematics and Society (MMS 2023),University of M’sila and ENS Bousaada

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.

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Hellal ABDELAZIZ , ,(2022-05-16), Anisotropic Parabolic p-Laplacian Equations,Journée Scientifique des Mathématiques et de I'Informatique (JSMI2022),Djilali Bounaâma Khemis Milliana University

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.

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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

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.

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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

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.

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Hellal ABDELAZIZ , ADMIN Admin , ,(2022), On Anisotropic Parabolic Equations with Variable Nonlinearity,Rencontre d’Analyse Mathématiqueet ses Applications (RAMA),Université de M’Sila

I contributed greatly to success the 7th M’sila Conference on Mathematical Analysis (7th MCMA 2022) as a Member of the organizing committee.

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Hellal ABDELAZIZ , ,(2022), Certificate of Recognition,7th M’sila Conference on Mathematical Analysis,M'sila

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.

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Hellal ABDELAZIZ , ,(2022), Some Regularity Results for a Singular Elliptic Equations with Variable Exponents,6th M'SILA Conference on Mathematical Analysis,M'Sila

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.

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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

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.

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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

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).

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Hellal ABDELAZIZ , ,(2020), On solutions of nonlinear elliptic equations with variable exponents and irregular data,ICRAMCS 2020,Casablanca, Morocco

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.

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Hellal ABDELAZIZ , ,(2019), ON p(·)-LAPLACIAN EQUATIONS WITH VARIABLE EXPONENTS AND L^m DATA,JAMA’19,Ziane Achour-Djelfa University

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.

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Hellal ABDELAZIZ , ,(2018), Nonlinear elliptic equation with variable exponents and measure data,MATHEMATICAL DAYS V,M'sila

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.

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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

University of Sciences and Technology Houari Boumediene BP 32 EL ALIA, Bab Ezzouar, Algiers, 16111, Algeria

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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

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

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Hellal ABDELAZIZ , ,(2010), Our contribution without paper,Premières Journées Scientifiques du LEM2I,MUNATEC, Tipaza, Algeria.