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Blow-up techniques and regularity near the boundary for free discontinuity problems. (English) Zbl 1044.49026
Summary: In this paper we exploit some compactness properties of the set of quasiminimizers of a functional with free discontinuities with the aim of obtaining blow-up techniques. These techniques are finally applied to show regularity near the boundary of the minimizers of the Mumford-Shah functional.

MSC:
49N60 Regularity of solutions in optimal control
49J45 Methods involving semicontinuity and convergence; relaxation
49J10 Existence theories for free problems in two or more independent variables
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