Higher integrability result for nonlinear elliptic systems with conormal boundary conditions. (May 2020)

• Record Type: Journal Article
• Authors: Kim, Youchan; Ryu, Seungjin; Shin, Pilsoo
• Is Part Of: Nonlinear analysis. Volume 194(2020)
• Publication Date: 2020-05
• Subjects: primary 35J47 35J60 -- secondary 35B65 35R05; Nonlinear elliptic system -- Higher integrability; 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.2018.12.017
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove a boundary higher integrability result for nonlinear elliptic systems with conormal boundary conditions in locally uniform domains. To do it, we derive a boundary version of Gehring–Giaquinta–Modica Lemma and Sobolev–Poincaré type inequality in locally uniform domains. Our result plays a key role for handling the coefficients when obtaining Calderó n–Zygmund type estimates with conormal boundary conditions in nonsmooth domains.