Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries

Caffarelli, L.¹ ; Lin, Fang-Hua²

¹ Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
² Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012

Journal of the American Mathematical Society, Tome 21 (2008) no. 3, pp. 847-862

Résumé

Here we study the asymptotic limits of solutions of some singularly perturbed elliptic systems. The limiting problems involve multiple valued harmonic functions or, in general, harmonic maps to singular spaces and free interfaces between supports of various components of the maps. The main results of the paper are the uniform Lipschitz regularity of solutions as well as the regularity of free interfaces.

Détail

DOI : 10.1090/S0894-0347-08-00593-6

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