Stability of solutions to obstacle problems with generalized Orlicz growth

TL;DR

This paper investigates the stability of solutions to obstacle problems with generalized Orlicz growth, proving convergence of solutions under operator limits in Sobolev and Hölder norms.

Contribution

It establishes the stability and convergence of solutions to nonlinear equations with Musielak–Orlicz growth under operator perturbations.

Findings

Solutions converge in Sobolev norms

Solutions converge in Hölder norms

Stability holds under local uniform convergence of operators

Abstract

We consider nonlinear equations having generalized Orlicz growth (also known as Musielak--Orlicz growth). We prove that if differential operators $\mathcal{A}_i$ converge locally uniformly to an operator $\mathcal{A}$, then the sequence of solutions $(u_i)$ has a subsequence converging to solution $u$ of the limit operator in Sobolev and H\"older norms.