Entropy solutions of anisotropic elliptic nonlinear obstacle problem with measure data

Salmani, Abdelhafid; Akdim, Youssef; Redwane, Hicham

doi:10.1007/s11587-019-00452-0

Cited by 7 publications

(3 citation statements)

References 12 publications

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“…and the right-hand side is a bounded Radon measure on Ω. In addition this, we mention some works in this direction such as [5,8,12,16,6,18].…”

Section: Introductionmentioning

confidence: 98%

“…In this study we are using the entropy solutions who was introduced for the first time by P. Benilan et al [7], because the function φ i does not belongs to L 1 loc (Ω) in general, then the problem (1.1) does not admit weak solution. In the case of a datum in µ ∈ L 1 (Ω) + W −1, − → p ′ (Ω) the existence of entropy solutions is treated by A. Salmani, Y. Akdim and H. Redwane in [16]. Moreover, L. Boccardo, T. Gallouet and L. Orsina (see [11]) have considered the case φ ≡ 0.…”

Section: Introductionmentioning

confidence: 99%

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Existence of entropy solutions of the anisotropic elliptic nonlinear problem with measure data in weighted Sobolev space

Abbassi¹,

Allalou²,

Kassidi³

2022

bspm

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This paper is devoted to study the following nonlinear anisotropic elliptic unilateral problem\begin{equation*}\begin{cases}A\,u -\mbox{div}\,\phi(u)=\mu \quad \mbox{in} \qquad \Omega \\\;u=0 \qquad \mbox{on} \quad \partial \Omega ,\end{cases}\end{equation*}where the right hand side $\,\mu\;$ belongs to $\; L^1(\Omega)+ W_{0}^{-1,\overrightarrow{p}'} (\Omega,\ \overrightarrow{\omega}^*)$. The operator $\displaystyle A\,u=-\sum_{i=1}^{N}\partial_{i}\,a_{i}(x,\ u,\ \nabla u)$ is a Leray-Lions anisotropic operator acting from $\; W_{0}^{1,\overrightarrow{p}} (\Omega,\ \overrightarrow{\omega})\;$ into its dual $\; W_{0}^{-1,\overrightarrow{p}'} (\Omega,\ \overrightarrow{\omega}^*)$ and $\phi_{i}\in C^{0}(\mathbb{R},\mathbb{R})$.

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“…and the right-hand side is a bounded Radon measure on Ω. In addition this, we mention some works in this direction such as [5,8,12,16,6,18].…”

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Existence of entropy solutions of the anisotropic elliptic nonlinear problem with measure data in weighted Sobolev space

Abbassi¹,

Allalou²,

Kassidi³

2022

bspm

View full text Add to dashboard Cite

show abstract

“…The aim of this paper is to extend the results in [5] to the anisotropic obstacle nonlinear elliptic problem. We want to prove only existence results, the uniqueness problem being a rather delicate one, this kind of problems still attracting the interest of the researchers (see [10,11,15] for a survey). One of the motivations for studying (P ) comes from applications to elasticity as the equations that models the shape of an elastic membrane which is pushed by an obstacle from one side affecting its shape.…”

Section: Introductionmentioning

confidence: 99%