Calculus of Variations and Geometric Measure Theory
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M. Colombo - G. Mingione

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 $a(\cdot)\geq 0$.


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