Entropy and renormalized solutions for some nonlinear anisotropic elliptic equations with variable exponents and <i>L</i>
                  <sup>1</sup>-data

Moumni, Mostafa El; Mohamed, Deval Sidi

doi:10.2478/mjpaa-2021-0018

Cited by 1 publication

(4 citation statements)

References 35 publications

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“…(2) Te main result of this study extends the previous works in [25,32] in the context of anisotropic space with variable exponent.…”

Section: Discussionsupporting

confidence: 79%

“…Reasoning as in [25] (see also [21,32]), we can prove that the operator A ϵ is pseudomonotone, coercive, and bounded. Ten, we deduce from [38] (Teorem 2.7) that A ϵ is surjective.…”

Section: Existence Results For L ' -Datamentioning

confidence: 76%

“…In this paper, we extend the recent works [21,24,25,32] by using the ideas developed in [21,32]. More precisely, we used the technic of monotone operators in Banach spaces and approximation methods to prove the existence and uniqueness of a renormalized solution of problem (E, f) in the context of anisotropic space involving variable exponents W 1, p → (.)…”

Section: Introductionmentioning

confidence: 99%

“…In the literature, special cases of problem (E, f) have been explored in the framework of anisotropic Sobolev space (see [23][24][25]) and have concerned the problem below:…”

Section: Introductionmentioning

confidence: 99%

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Existence and Uniqueness of Renormalized Solution to Nonlinear Anisotropic Elliptic Problems with Variable Exponent and $L^{1}$ -Data

Konaté¹,

Ouedraogo

2023

International Journal of Differential Equations

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Nonlinear partial differential equations are considered as an essential tool for describing the behavior of many natural phenomena. The modeling of some phenomena requires to work in Sobolev spaces with constant exponent. But for others, such as electrorheological fluids, the properties of classical spaces are not sufficient to have precision. To overcome this difficulty, we work in the appropriate spaces called Lebesgue and Sobolev spaces with variable exponent. In recent works, researchers are attracted by the study of mathematical problems in the context of variable exponent. This great interest is motivated by their applications in many fields such as elastic mechanics, fluid dynamics, and image restoration. In this paper, we combine the technic of monotone operators in Banach spaces and approximation methods to prove the existence of renormalized solutions of a class of nonlinear anisotropic problem involving p ⟶ . − Leray–Lions operator, a graph, and L 1 data. In particular, we establish the uniqueness of the solution when the graph data are considered a strictly increasing function.

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“…(2) Te main result of this study extends the previous works in [25,32] in the context of anisotropic space with variable exponent.…”

Section: Discussionsupporting

confidence: 79%

“…Reasoning as in [25] (see also [21,32]), we can prove that the operator A ϵ is pseudomonotone, coercive, and bounded. Ten, we deduce from [38] (Teorem 2.7) that A ϵ is surjective.…”

Section: Existence Results For L ' -Datamentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

“…In the literature, special cases of problem (E, f) have been explored in the framework of anisotropic Sobolev space (see [23][24][25]) and have concerned the problem below:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Existence and Uniqueness of Renormalized Solution to Nonlinear Anisotropic Elliptic Problems with Variable Exponent and $L^{1}$ -Data

Konaté¹,

Ouedraogo

2023

International Journal of Differential Equations

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Entropy and renormalized solutions for some nonlinear anisotropic elliptic equations with variable exponents and L ¹-data

Abstract: We prove in this paper some existence and unicity results of entropy and renormalized solutions for some nonlinear elliptic equations with general anisotropic diffusivities and variable exponents. The data are assumed to be merely integrable.

Cited by 1 publication

References 35 publications

Existence and Uniqueness of Renormalized Solution to Nonlinear Anisotropic Elliptic Problems with Variable Exponent and $L^{1}$ -Data

Existence and Uniqueness of Renormalized Solution to Nonlinear Anisotropic Elliptic Problems with Variable Exponent and $L^{1}$ -Data

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Entropy and renormalized solutions for some nonlinear anisotropic elliptic equations with variable exponents and L 1-data

Abstract: We prove in this paper some existence and unicity results of entropy and renormalized solutions for some nonlinear elliptic equations with general anisotropic diffusivities and variable exponents. The data are assumed to be merely integrable.

Cited by 1 publication

References 35 publications

Existence and Uniqueness of Renormalized Solution to Nonlinear Anisotropic Elliptic Problems with Variable Exponent and L 1 -Data

Existence and Uniqueness of Renormalized Solution to Nonlinear Anisotropic Elliptic Problems with Variable Exponent and L 1 -Data

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Entropy and renormalized solutions for some nonlinear anisotropic elliptic equations with variable exponents and L ¹-data

Existence and Uniqueness of Renormalized Solution to Nonlinear Anisotropic Elliptic Problems with Variable Exponent and $L^{1}$ -Data

Existence and Uniqueness of Renormalized Solution to Nonlinear Anisotropic Elliptic Problems with Variable Exponent and $L^{1}$ -Data