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

Caffarelli, L.; Lin, Fang-Hua

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

Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries
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by L. A. Caffarelli and Fang-Hua Lin

J. Amer. Math. Soc. 21 (2008), 847-862

DOI: https://doi.org/10.1090/S0894-0347-08-00593-6

Published electronically: February 12, 2008

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Abstract:

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.

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