Calculus of Variations and Geometric Measure Theory

G. Leoni - M. Morini

Some Remarks on the Analyticity of Minimizers of Free Discontinuity Problems

created on 11 Nov 2002
modified on 05 Sep 2003


Published Paper

Inserted: 11 nov 2002
Last Updated: 5 sep 2003

Journal: J. Math. Pures Appl.
Volume: 82
Pages: 533 - 551
Year: 2003


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.