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Publication 02-CNA-25

Some Remarks on the Analyticity of Minimizers of Free Discontinuity Problems

Giovanni Leoni
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

and

Massimiliano Morini
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

Abstract: In this paper we give a partial answer to a conjecture of De Giorgi, namely we prove that in dimension two the regular part of the discontinuity set of a local minimizer of the homogeneous Mumford-Shah functional is analytic with the excpetion of at most a countable number of isolated points.

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