Calderón–Zygmund estimates and non-uniformly elliptic operators

We consider a class of non-uniformly nonlinear elliptic equations whose model is given by−div(|Du|p−2Du+a(x)|Du|q−2Du)=−div(|F|p−2F+a(x)|F|q−2F) where p<q and a(x)≥0, and establish the related nonlinear Calderón–Zygmund theory. In particular, we provide sharp conditions under which the natural, a...

Full description

Saved in:
Bibliographic Details
Published inJournal of functional analysis Vol. 270; no. 4; pp. 1416 - 1478
Main Authors Colombo, Maria, Mingione, Giuseppe
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.02.2016
Subjects
Calderón–Zygmund estimates
Degenerate operators
Non-uniform ellipticity
Regularity
Degenerate operators
Non-uniform ellipticity
Regularity
35D10
35J70
Calderón–Zygmund estimates
Online AccessGet full text

Cover

More Information
Summary:We consider a class of non-uniformly nonlinear elliptic equations whose model is given by−div(|Du|p−2Du+a(x)|Du|q−2Du)=−div(|F|p−2F+a(x)|F|q−2F) where p<q and a(x)≥0, and establish the related nonlinear Calderón–Zygmund theory. In particular, we provide sharp conditions under which the natural, and optimal, Calderón–Zygmund type result(|F|p+a(x)|F|q)∈Llocγ⟹(|Du|p+a(x)|Du|q)∈Llocγ holds for every γ≥1. These problems naturally emerge as Euler–Lagrange equations of some variational integrals introduced and studied by Marcellini [41] and Zhikov [53] in the framework of Homogenisation and Lavrentiev phenomenon.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2015.06.022