Morrey regularity for nonlinear elliptic equations with partial BMO nonlinearities under controlled growth. (March 2019)

• Record Type: Journal Article
• Authors: Tian, Hong; Zheng, Shenzhou
• Is Part Of: Nonlinear analysis. Volume 180(2019)
• Page Start: 1
• Page End: 19
• Publication Date: 2019-03
• Subjects: 35J25 -- 35J60; Nonlinear elliptic equations -- Controlled growth -- Morrey regularity -- Partially BMO nonlinearities -- Reifenberg flat domains; 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.2018.09.007
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove a global Morrey regularity for the gradients of weak solution to nonlinear elliptic equations under controlled growth with partial BMO nonlinearities in x -variables over Reifenberg flat domains. We mainly suppose that the principal nonlinearity is merely measurable in one variable and has a small BMO seminorm in the remaining variables; while the lower order terms are subjected to the so-called controlled growth of the gradients, and the boundary of underlying domain is sufficiently flat in the sense of Reifenberg.