Abstract

This paper contains existence and regularity results for solutions u from Ω to RnN\mathbb{R}^{n^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

Author information

Contact details are reproduced from the original publication and may be historical.

Nicola Fusco

Dip. di Matematica, Università di Napoli, Complesso Monte S. Angelo, 80126 Napoli, Italy

Giuseppe Mingione

Dip. di Matematica, Università di Parma, Via Massimo D'Azeglio 85/A, 43100 Parma, Italy

Cristina Trombetti

Dip. di Matematica, Università di Napoli, Complesso Monte S. Angelo, 80126 Napoli, Italy

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Suggested citation

N. Fusco, G. Mingione, C. Trombetti. “Regularity of Minimizers for a Class of Anisotropic Free Discontinuity Problems.” Journal of Convex Analysis 8 (2001), No. 2, 349–367. https://doi.org/10.68381/jca08017

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Published by Heldermann Verlag, 2001. Rights now held by Banach Press LLC.