Stability of solutions to obstacle problems with generalized Orlicz growth

Abstract

Abstract We consider nonlinear equations having generalized Orlicz growth (also known as Musielak–Orlicz growth). We prove that if differential operators 𝒜 i {\mathcal{A}_{i}} converge locally uniformly to an operator 𝒜 {\mathcal{A}} , then the sequence of solutions ( u i ) {(u_{i})} has a subsequence converging to the solution u of the limit operator in Sobolev and Hölder norms.