Premium
On optimal regularity of free boundary problems and a conjecture of De Giorgi
Author(s) -
Koch Herbert,
Leoni Giovanni,
Morini Massimiliano
Publication year - 2005
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20065
Subject(s) - conjecture , mathematics , boundary (topology) , class (philosophy) , pure mathematics , nonlinear system , boundary value problem , mathematical analysis , epistemology , philosophy , physics , quantum mechanics
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. © 2004 Wiley Periodicals, Inc.