Stability of solutions to obstacle problems with generalized Orlicz growth

2022/03/25 by Petteri Harjulehto, Harjulehto, Petteri, Arttu Karppinen +1
Computer Science · Mathematics · #35B20 #35J25 #35J60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2203.13624

openalex publication_date 2022/03/25 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

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

Related

• Global continuity and higher integrability of a minimizer of an obstacle\n problem under generalized Orlicz growth conditions
• Global continuity and higher integrability of a minimizer of an obstacle problem under generalized Orlicz growth conditions
• H "older continuity of the minimizer of an obstacle problem with\n generalized Orlicz growth
• Obstacle problem for a class of parabolic equations of generalized\n p-Laplacian type
• Wolff potential estimates for elliptic obstacle problems with generalized Orlicz growth