Gradient estimates for double phase problems with irregular obstacles. (December 2018)

• Record Type: Journal Article
• Authors: Byun, Sun-Sig; Cho, Yumi; Oh, Jehan
• Is Part Of: Nonlinear analysis. Volume 177(2018)Part A
• Page Start: 169
• Page End: 185
• Publication Date: 2018-12
• Subjects: primary 35J87 -- secondary 35B65; Calderón–Zygmund estimate -- Double phase problem -- Obstacle problem; 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.2018.02.008
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: An irregular obstacle problem with non-uniformly elliptic operator in divergence form of ( p, q ) -growth is studied. We find an optimal regularity for such a double phase obstacle problem by essentially proving that the gradient of a solution is as integrable as both the gradient of the assigned obstacle function and the associated nonhomogeneous term in the divergence. Calderón–Zygmund type estimates are also obtained under minimal regularity requirements of the prescribed data.