# Regularity for double phase variational problems

created by mingione on 14 Aug 2014
modified on 12 Jan 2015

[BibTeX]

Published Paper

Inserted: 14 aug 2014
Last Updated: 12 jan 2015

Journal: Arch. Rat. Mech. Anal.
Volume: 215
Pages: 443-496
Year: 2015
Doi: 10.1007/s00205-014-0785-2

Abstract:

We prove sharp regularity theorems for minimisers of a class of variational integrals whose integrand switches between two different types of degenerate elliptic phases, according to the zero set of a modulating coefficient $a(\cdot)$. The model case is given by the functional $w \to \int (\ Dw\ ^p+a(x)\ Dw\ ^q) \, dx\;,$ where $q>p$ and $a(\cdot)\geq 0$.