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2010, Volume 28, Issue 3: 915-929. Doi: 10.3934/dcds.2010.28.915
This issue Previous Article Partial regularity for elliptic equations Next Article Analytical, geometrical and topological aspects of a class of mean field equations on surfaces

Analysis on the junctions of domain walls

  • 1.

    University of Texas at Austin, Department of Mathematics, 1 University Station, C1200, Austin, TX 78712-1082

  • 2.

    Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185

Received:  February 28, 2010
Revised:  March 31, 2010
Published:  August 2010
Abstract Related Papers Cited by
    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.
    Mathematics Subject Classification: 35R35; 49R99.

    Citation:
    shu

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