TY - JOUR
T1 - The Obstacle Problem for Nonlinear Degenerate Elliptic Equations with Variable Exponents and $L^1$-Data
AU - Khelifi , Hichem
JO - Journal of Partial Differential Equations
VL - 2
SP - 101
EP - 122
PY - 2022
DA - 2022/04
SN - 35
DO - http://doi.org/10.4208/jpde.v35.n2.1
UR - https://global-sci.org/intro/article_detail/jpde/20444.html
KW - Ostacle problem, Degenerate Coercivity, Variable exponents, $L^1$ data, Truncation function.
AB - <p style="text-align: justify;">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 $q(\cdot)&gt;1$.</p>