Luis A. Caffarelli - University of Texas at Austin, Department of Mathematics, 1 University Station, C1200, Austin, TX 78712-1082, United States (email)
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: free boundaries; calculus of
variations; montonicity formula.
Received: March 2010; Revised: April 2010; Published: April 2010.
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