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

Bounded minimisers of double phase variational integrals

created by mingione on 24 Feb 2015
modified on 28 Jun 2015

[BibTeX]

Published Paper

Inserted: 24 feb 2015
Last Updated: 28 jun 2015

Journal: Arch. Rat. Mech. Anal.
Volume: 218
Pages: 219-273
Year: 2015
Doi: 10.1007/s00205-015-0859-9
Links: paper

Abstract:

Bounded minimisers of the functional \[ w \to \int (\
Dw\
^p+a(x)\
Dw\
^q) \, dx\;, \] where $0\leq a(\cdot) \in C^{0, \alpha}$ and $1< p < q$, are $C^{1, \beta}$-regular provided the sharp bound \[ q \leq p+\alpha \] holds.

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