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

Koch Herbert | Zendy; Leoni Giovanni | Zendy; Morini Massimiliano | Zendy

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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.

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