Existence of solutions for degenerate elliptic problems in weighted Sobolev space
Summary: This paper is devoted to the study of the existence of solutions to a general elliptic problem \(Au+g(x,u,\nabla u)=f-\mathrm{div} F\), with \(f\in L^1(\Omega)\) and \(F\in\prod_{i=1}^NL^{p'}(\Omega,\omega_i^\ast)\), where \(A\) is a Leray-Lions operator from a weighted Sobolev space into its dual and \(g(x,s,\xi)\) is a nonlinear term satisfying \(g(x,s,\xi)\mathrm{sgn}(s)\geq\rho\sum_{i=1}^N\omega_i|\xi_i|p\), \(|s|\geq h>0\), and a growth condition with respect to \(\xi\). Here, \(\omega_i\), \(\omega_i^\ast\) are weight functions that will be defined in the Preliminaries.
scientific article; zbMATH DE number 6529022