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

✍ Scribed by Herbert Koch; Giovanni Leoni; Massimiliano Morini

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
195 KB
Volume
58
Category
Article
ISSN
0010-3640

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✦ Synopsis

Abstract

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. Β© 2004 Wiley Periodicals, Inc.

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