Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries
- 12 February 2008
- journal article
- Published by American Mathematical Society (AMS) in Journal of the American Mathematical Society
- Vol. 21 (3) , 847-862
- https://doi.org/10.1090/s0894-0347-08-00593-6
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.Keywords
This publication has 19 references indexed in Scilit:
- An Optimal Partition Problem for EigenvaluesJournal of Scientific Computing, 2006
- Uniform Hölder Estimates in a Class of Elliptic Systems and Applications to Singular Limits in Models for Diffusion FlamesArchive for Rational Mechanics and Analysis, 2006
- Segregated nodal domains of two-dimensional multispecies Bose–Einstein condensatesPhysica D: Nonlinear Phenomena, 2004
- An optimal partition problem related to nonlinear eigenvaluesJournal of Functional Analysis, 2003
- Nehari's problem and competing species systemsAnnales de l'Institut Henri Poincaré C, Analyse non linéaire, 2002
- N-Dimensional Shape Optimization under Capacitary ConstraintJournal of Differential Equations, 1995
- An existence result for a class of shape optimization problemsArchive for Rational Mechanics and Analysis, 1993
- Shape optimization for Dirichlet problems: Relaxed formulation and optimality conditionsApplied Mathematics & Optimization, 1991
- 𝑄 valued functions minimizing Dirichlet’s integral and the regularity of area minimizing rectifiable currents up to codimension twoBulletin of the American Mathematical Society, 1983
- Diffusion FlamesIndustrial & Engineering Chemistry, 1928