Journal of Convex Analysis 08 (2001), No. 2, 349--368
Copyright Heldermann Verlag 2001
Regularity of Minimizers for a Class of Anistropic Free Discontinuity Problems
Nicola Fusco
Dip. di Matematica, Universitą di Napoli, Complesso Monte S. Angelo, 80126 Napoli, Italy
Giuseppe Mingione
Dip. di Matematica, Universitą di Parma, Via Massimo D'Azeglio 85/A, 43100 Parma, Italy
Cristina Trombetti
Dip. di Matematica, Universitą di Napoli, Complesso Monte S. Angelo, 80126 Napoli, Italy
This paper contains existence and regularity results for solutions u from Ω to (Rn)N of a class of free discontinuity 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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