The Obstacle Problem for Nonlinear Degenerate Elliptic Equations with Variable Exponents and $L^1$-Data
Year: 2022
Author: Hichem Khelifi
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 2 : pp. 101–122
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v35.n2.1
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 2 : pp. 101–122
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Ostacle problem Degenerate Coercivity Variable exponents $L^1$ data Truncation function.