Weak solutions to strongly nonlinear weighted degenerate inclusion problems with <i>L</i> ¹ -data

This paper is devoted to the analysis of a broad class of strongly nonlinear elliptic differential inclusion problems of Leray–Lions type within the framework of weighted Sobolev spaces, under degenerate coercivity and driven by L1-data. Our approach combines Yosida regularization with truncation techniques specifically adapted to the weighted Sobolev setting. We first establish the existence of weak solutions for bounded data, and subsequently derive the existence of weak solutions for general L1-data.