Calculus of Variations and Geometric Measure Theory

H. Koch - G. Leoni - M. Morini

On optimal regularity of free boundary problems and a conjecture of De Giorgi

created on 11 Jan 2004
modified by leoni on 29 Jul 2005


Published Paper

Inserted: 11 jan 2004
Last Updated: 29 jul 2005

Journal: Communications on Pure and Applied Mathematics
Volume: 58
Pages: 1051-1076
Year: 2005


We present a general theory to study optimal regularity for a large class of nonlinear elliptic systems satisfying general boundary conditions and in the presence of a geometric transmission condition on the free-boundary. As an application we give a full positive answer to a conjecture of De Giorgi on the analyticity of local minimizers of the Mumford-Shah functional.

Keywords: free discontinuity problems, Mumford-Shah functional, free boundary problems, analyticity