Inserted: 11 jan 2004
Last Updated: 29 jul 2005
Journal: Communications on Pure and Applied Mathematics
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.