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


Authors: L. A. Caffarelli and Fang-Hua Lin
Journal: J. Amer. Math. Soc. 21 (2008), 847-862
MSC (2000): Primary 35B25, 35P30, 49N60
DOI: https://doi.org/10.1090/S0894-0347-08-00593-6
Published electronically: February 12, 2008
MathSciNet review: 2393430
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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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Additional Information

L. A. Caffarelli
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Email: caffarel@math.utexas.edu

Fang-Hua Lin
Affiliation: Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012
Email: linf@cims.nyu.edu

DOI: https://doi.org/10.1090/S0894-0347-08-00593-6
Keywords: Singular limit, regularity of free interface, multiple-valued harmonic functions, harmonic maps.
Received by editor(s): August 24, 2006
Published electronically: February 12, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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