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

Journal of Partial Differential Equations
Vol. 35 No. 2 (2022), pp. 101-122
DOI: 10.4208/jpde.v35.n2.1
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Author(s)
    Hichem Khelifi
    Department of Mathematics and Informatics, University of Algiers, Algiers, Algeria. 2 Street Didouche Mourad Algiers. Univ Algiers, Dept Math, Lab LEDPNL, HM,ENS Kouba, Algeria 2 St Didouche Mourad Algiers, Alger Ctre, Algeria
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1 Department of Mathematics and Informatics, University of Algiers, Algiers, Algeria. 2 Street Didouche Mourad Algiers.
2 Univ Algiers, Dept Math, Lab LEDPNL, HM,ENS Kouba, Algeria 2 St Didouche Mourad Algiers, Alger Ctre, Algeria
Received
April 22, 2021
Accepted
June 28, 2021
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 $q(\cdot)>1$.

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