The Obstacle Problem for Nonlinear Degenerate Elliptic Equations with Variable Exponents and $L^1$-Data (Journal of Partial Differential Equations, 2022)
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 $W^{1,q(·)}(Ω)$ with some $q(·)>1$.
Keywords: Ostacle problem; Degenerate Coercivity; Variable exponents; $L^1$ data; Truncation function.