%0 Journal Article
%T Existence of energy-minimal diffeomorphisms between doubly connected domains
%A Tadeusz Iwaniec
%A Ngin-Tee Koh
%A Leonid V. Kovalev
%A Jani Onninen
%J Mathematics
%D 2010
%I arXiv
%R 10.1007/s00222-011-0327-6
%X The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Specifically, among all homeomorphisms f : R -> R* between bounded doubly connected domains such that Mod (R) < Mod (R*) there exists, unique up to conformal authomorphisms of R, an energy-minimal diffeomorphism. No boundary conditions are imposed on f. Although any energy-minimal diffeomorphism is harmonic, our results underline the major difference between the existence of harmonic diffeomorphisms and the existence of the energy-minimal diffeomorphisms. The existence of globally invertible energy-minimal mappings is of primary pursuit in the mathematical models of nonlinear elasticity and is also of interest in computer graphics.
%U http://arxiv.org/abs/1008.0652v1