Analysis on the junctions of domain walls

Luis A. Caffarelli; Fang Hua Lin

doi:10.3934/dcds.2010.28.915

Analysis on the junctions of domain walls

Luis A. Caffarelli, Fang Hua Lin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study the local structure and the smoothness of singularities of free boundaries in an optimal partition problem for the Dirichlet eigenvalues. We prove that there is a unique homogeneous blow up(tangent map) at each singular point in the interior of the free boundary. As a consequence we obtain the rectifiability as well as local structures of singularities.

Original language	English (US)
Pages (from-to)	915-929
Number of pages	15
Journal	Discrete and Continuous Dynamical Systems
Volume	28
Issue number	3
DOIs	https://doi.org/10.3934/dcds.2010.28.915
State	Published - Nov 2010

Keywords

Calculus of variations
Free boundaries
Montonicity formula

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2010.28.915

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title = "Analysis on the junctions of domain walls",

abstract = "In this paper, we study the local structure and the smoothness of singularities of free boundaries in an optimal partition problem for the Dirichlet eigenvalues. We prove that there is a unique homogeneous blow up(tangent map) at each singular point in the interior of the free boundary. As a consequence we obtain the rectifiability as well as local structures of singularities.",

keywords = "Calculus of variations, Free boundaries, Montonicity formula",

author = "Caffarelli, {Luis A.} and Lin, {Fang Hua}",

year = "2010",

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AB - In this paper, we study the local structure and the smoothness of singularities of free boundaries in an optimal partition problem for the Dirichlet eigenvalues. We prove that there is a unique homogeneous blow up(tangent map) at each singular point in the interior of the free boundary. As a consequence we obtain the rectifiability as well as local structures of singularities.

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KW - Montonicity formula

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Analysis on the junctions of domain walls

Abstract

Keywords

ASJC Scopus subject areas

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