The Obstacle Problem for Nonlinear Degenerate Elliptic Equations with Variable Exponents and $L^1$-Data

Hichem Khelifi

doi:10.4208/jpde.v35.n2.1

The Obstacle Problem for Nonlinear Degenerate Elliptic Equations with Variable Exponents and $L^1$-Data

Authors

Hichem Khelifi Department of Mathematics and Informatics, University of Algiers, Algiers, Algeria. 2 Street Didouche Mourad Algiers.

DOI:

https://doi.org/10.4208/jpde.v35.n2.1

Keywords:

Ostacle problem, Degenerate Coercivity, Variable exponents, $L^1$ data, Truncation function.

Abstract

The aim of this paper is to study the obstacle problem associated with an elliptic operator having degenerate coercivity, and $L^{1}-$data. The functional setting involves Lebesgue-Sobolev spaces with variable exponents. We prove the existence of an entropy solution and show its continuous dependence on the $L^{1}-$data in $W^{1,q(\cdot)}(\Omega)$ with some $q(\cdot)>1$.

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Published

2022-04-14

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Issue

Vol. 35 No. 2 (2022)

Section

Articles

How to Cite

The Obstacle Problem for Nonlinear Degenerate Elliptic Equations with Variable Exponents and $L^1$-Data. (2022). Journal of Partial Differential Equations, 35(2), 101-122. https://doi.org/10.4208/jpde.v35.n2.1