Analysis on the junctions of domain walls

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July 2010, 28(3): 915-929. doi: 10.3934/dcds.2010.28.915

Analysis on the junctions of domain walls

Luis A. Caffarelli ^1, and Fang Hua Lin ^2,

1.	University of Texas at Austin, Department of Mathematics, 1 University Station, C1200, Austin, TX 78712-1082, United States
2.	Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185, United States

Received March 2010 Revised April 2010 Published April 2010

Abstract
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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: free boundaries; calculus of variations; montonicity formula..

Mathematics Subject Classification: 35R35; 49R9.

Citation: Luis A. Caffarelli, Fang Hua Lin. Analysis on the junctions of domain walls. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 915-929. doi: 10.3934/dcds.2010.28.915

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