Analysis on the junctions of domain walls
Luis A. Caffarelli, Fang Hua Lin · Discrete and Continuous Dynamical Systems · 2010
In this paper, we study the local structure and the smoothness ofsingularities of free boundaries in an optimal partition problem forthe Dirichlet eigenvalues. We prove that there is a uniquehomogeneous blow up(tangent map) at each singular point in theinterior of the free boundary. As a consequence we obtain therectifiability as well as local structures of singularities.