Global Calderón–Zygmund theory for nonlinear elliptic obstacle problems with asymptotically regular nonlinearities. (August 2015)

• Record Type: Journal Article
• Authors: Byun, Sun-Sig; Cho, Yumi; Oh, Jehan
• Is Part Of: Nonlinear analysis. Volume 123/124(2015)
• Page Start: 150
• Page End: 157
• Publication Date: 2015-08
• Subjects: primary 35J60 -- secondary 35R05; Asymptotically regular -- Obstacle problem -- Calderón–Zygmund estimates -- Discontinuous nonlinearity -- BMO -- Reifenberg domain; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.05.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study a nonlinear elliptic problem with an irregular obstacle in a bounded nonsmooth domain when the nonlinearity is merely asymptotically regular. We find an optimal regularity requirement on the associated nonlinearity and a minimal geometric condition on the boundary to ensure a global Calderón–Zygmund estimate for such an asymptotically regular obstacle problem. We assume that the associated nonlinearity has a small BMO and the boundary is sufficiently flat in the Reifenberg sense.