Regularity of Minimizers for a Class of Anisotropic Free Discontinuity Problems

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