Analysis on the junctions of domain walls

Pages: 915 - 929, Volume 28, Issue 3, November 2010

doi:10.3934/dcds.2010.28.915       Abstract        Full Text (223.4K)       Related Articles

Luis A. Caffarelli - University of Texas at Austin, Department of Mathematics, 1 University Station, C1200, Austin, TX 78712-1082, United States (email)
Fang Hua Lin - Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185, 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.
Mathematics Subject Classification:  35R35; 49R99.

Received: March 2010;      Revised: April 2010;      Published: April 2010.