The obstacle problem for degenerate anisotropic elliptic equations with variable exponents and $L^1$-data

Abstract

In this paper, we prove the existence of entropy solutions for the obstacle problem associated with nonlinear degenerate anisotropic elliptic equations with L 1 -data. The functional framework involves anisotropic Sobolev spaces with variable exponents as well as weak Lebesgue (Marcinkiewicz) spaces with variable exponents. Our results are a natural generalization of some existing ones in the context of constant isotropic exponents.