Calculus of Variations and Geometric Measure Theory
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N. Fusco - G. Mingione - C. Trombetti

Regularity of minimizers for a class of anisotropic free discontinuity problems

created by mingione on 29 Sep 2012


Published Paper

Inserted: 29 sep 2012

Journal: J. Convex Anal.
Volume: 8
Pages: 349-367
Year: 2001


This paper contains existence and regularity results for solutions $u : \Omega \to R^{Nn}$ of a class of free disconti- nuity problems i.e.: the energy to minimize consists of both a bulk and a surface part. The main feature of the class of problems considered here is that the energy density of the bulk part is supposed to be fully anisotropic with p-growth in the scalar case, $N = 1$. Similar results for the vectorial case $N > 1$ are obtained for radial energy densities, being anisotropic again with p-growth.

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