On some p(x)-quasilinear problem with right-hand side measure

Azroul, Elhoussine; Benboubker, Mohamed Badr; Rhoudaf, M.

doi:10.1016/j.matcom.2013.09.009

Cited by 21 publications

(13 citation statements)

References 7 publications

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“…Otherwise, the term H(x, u, ∇u) is said to be an absorption term, in this case a detailed picture of what happens is available (see e.g. [4,6,8,9,10,11]). …”

Section: P(x)mentioning

confidence: 99%

“…We feel that the techniques needed to obtain the proofs of Lemma 3.1 and Lemma 3.3 can be done by a slight modifications of the corresponding ones in [7] and [4].…”

Section: Lemma 33 ( [4]) Let F : R → R Be a Uniformly Lipschitz Funmentioning

confidence: 99%

“…The paper of Sanchón and Urbano showed the way to study the notion of entropy solutions to problems in variable exponent spaces with Dirichlet homogeneous boundary-value conditions (see e.g. [3,4,5,6,17,23]). At the same time, the theory regarding the weighted Sobolev spaces with variable exponent p(x), i.e.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Existence of entropy solutions for degenerate elliptic unilateral problems with variable exponents

Azroul¹,

Barbara²,

Benboubker

et al. 2018

B Soc Paran Mat

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In this article, we study the following degenerate unilateral problems: $$ -\mbox{ div} (a(x,\nabla u))+H(x,u,\nabla u)=f,$$ which is subject to the Weighted Sobolev spaces with variable exponent $W^{1,p(x)}_{0}(\Omega,\omega)$, where $\omega$ is a weight function on $\Omega$, ($\omega$ is a measurable, a.e. strictly positive function on $\Omega$ and satisfying some integrability conditions). The function $H(x,s,\xi)$ is a nonlinear term satisfying some growth condition but no sign condition and the right hand side $f\in L^1(\Omega)$.

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“…Otherwise, the term H(x, u, ∇u) is said to be an absorption term, in this case a detailed picture of what happens is available (see e.g. [4,6,8,9,10,11]). …”

Section: P(x)mentioning

confidence: 99%

“…We feel that the techniques needed to obtain the proofs of Lemma 3.1 and Lemma 3.3 can be done by a slight modifications of the corresponding ones in [7] and [4].…”

Section: Lemma 33 ( [4]) Let F : R → R Be a Uniformly Lipschitz Funmentioning

confidence: 99%

See 1 more Smart Citation

Existence of entropy solutions for degenerate elliptic unilateral problems with variable exponents

Azroul¹,

Barbara²,

Benboubker

et al. 2018

B Soc Paran Mat

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“…Moreover, they have shown some regularity results. For other interesting existence and regularity results, we refer to [1,2,4].…”

Section: Introductionmentioning

confidence: 99%

Existence of entropy solutions for some nonlinear elliptic problems involving variable exponent and measure data

Ahmedatt

Azroul

Hjiaj

et al. 2018

bspm

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“…In the framework of variable exponent Sobolev spaces, we list the works [6,7,10,11] and others, where the second member µ of the problem (P ) is taking as an element of L 1 (Ω) or is a measure which admits the composition…”

Section: Introductionmentioning

confidence: 99%

Existence and Regularity of Solution for Strongly Nonlinear <em>p(x)</em>-Elliptic Equation with Measure Data

Cherif¹

2017

JPDE

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Abstract. The first part of this paper is devoted to study the existence of solution for nonlinear p(x) elliptic problem A(u) = µ in Ω, u = 0 on ∂Ω, with a right-hand side measure, where Ω is a bounded open set of R N , N 2 and(Ω) in to its dual W −1,p ′ (x) (Ω). However the second part concerns the existence solution, of the following setting nonlinear elliptic problems A(u)+ g (x,u,∇u) = µ in Ω, u = 0 on ∂Ω. We will give some regularity results for these solutions. AMS Subject Classifications: 35J20, 35J25, 35J60Chinese Library Classifications: O175.29

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On some p(x)-quasilinear problem with right-hand side measure

Cited by 21 publications

References 7 publications

Existence of entropy solutions for degenerate elliptic unilateral problems with variable exponents

Existence of entropy solutions for degenerate elliptic unilateral problems with variable exponents

Existence of entropy solutions for some nonlinear elliptic problems involving variable exponent and measure data

Existence and Regularity of Solution for Strongly Nonlinear <em>p(x)</em>-Elliptic Equation with Measure Data

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