Manifold-constrained free discontinuity problems and Sobolev approximation (Q6603996)

In this paper the authors study local minimizers of free-discontinuity problems of a Mumford-Shah and Griffith type, with a variable exponent growth and a manifold-valued constraint on maps, defined in a bounded two-dimensional domain. They will establish a Sobolev approximation result for special functions with small jump, and thus, establishing essential closedness of the jump sets and Hölderianity of minimizers.