Global continuity and higher integrability of a minimizer of an obstacle problem under generalized Orlicz growth conditions

2019/12/12 by Arttu Karppinen
Computer Science · Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Optimization and Variational Analysis

paper · doi:10.1007/s00229-019-01173-2

crossref issued 2019/12/12 · crossref published 2019/12/12 · crossref published-online 2019/12/12 · openalex publication_date 2019/12/12 · crossref created 2020/12/11 · crossref published-print 2021/01/01 · crossref deposited 2022/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29 · crossref indexed 2026/07/29

Abstract

Abstract We prove continuity up to the boundary of the minimizer of an obstacle problem and higher integrability of its gradient under generalized Orlicz growth. The result recovers similar results obtained in the special cases of polynomial growth, variable exponent growth and produces new results for Orlicz and double phase growth.

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