Global gradient estimates for spherical quasi-minimizers of integral functionals with p(x)-growth. (December 2018)

• Record Type: Journal Article
• Authors: Byun, Sun-Sig; Ok, Jihoon; Youn, Yeonghun
• Is Part Of: Nonlinear analysis. Volume 177(2018)Part A
• Page Start: 186
• Page End: 208
• Publication Date: 2018-12
• Subjects: primary 35J20 -- secondary 49N60; Spherical quasi minimizer -- Functional with p(x) growth -- Calderón–Zygmund estimates; 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.2018.01.017
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We investigate spherical quasi-minimizers (or so-called spherical Q -minimizers) u for integral functionals with p ( x ) -growth of F ( u, Ω ) ≔ ∫ Ω f ( x, D u ) − | G | p ( x ) − 2 G ⋅ D u d x . In particular, we find minimal regularity requirements on the integrand f ( x, ξ ), the variable exponent p ( x ), the boundary ∂ Ω of the bounded domain Ω as well as Q under which | G | p ( ⋅ ) ∈ L q ( Ω ) ⟹ | D u | p ( ⋅ ) ∈ L q ( Ω ) for every q ≥ 1 with the desired global Calderón–Zygmund estimate.