Calderón–Zygmund estimates for general elliptic operators with double phase. (May 2020)

• Record Type: Journal Article
• Authors: Shin, Pilsoo
• Is Part Of: Nonlinear analysis. Volume 194(2020)
• Publication Date: 2020-05
• Subjects: primary 35J70 -- secondary 35B65; Calderón–Zygmund estimates -- Non-uniform ellipticity -- General quasi-linear operator; 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.2018.12.020
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We derive Calderón–Zygmund type estimates for the gradient of bounded distributional solutions to the problem div b ( x, u ) | D u | p − 2 D u + a ( x ) | D u | q − 2 D u = div | F | p − 2 F + a ( x ) | F | q − 2 F where 1 < p < q and 0 ≤ a ( ⋅ ) ∈ C α . The coefficient b ( x, z ) is supposed to be small-BMO with respect to x and merely continuous in z .