Document Type
Article
Date
7-31-2011
Disciplines
Mathematics
Description/Abstract
Let X and Y be planar Jordan domains of the same finite connectivity, Y being inner chordarc regular (such are Lipschitz domains). Every homeomorphism h:X->Y in the Sobolev space W1,2 extends to a continuous map between closed domains. We prove that there exist homeomorphisms between closed domains which converge to h uniformly and in W1,2. The problem of approximation of Sobolev homeomorphisms, raised by J. M. Ball and L. C. Evans, is deeply rooted in a study of energy-minimal deformations in nonlinear elasticity. The new feature of our main result is that approximation takes place also on the boundary, where the original map need not be a homeomorphism.
Recommended Citation
Iwaniec, Tadeusz; Kovalev, Leonid V.; and Onninen, Jani, "Strong Approximation of Homeomorphisms of Finite Dirichlet Energy" (2011). Mathematics - All Scholarship. 56.
https://surface.syr.edu/mat/56
Source
Harvested from arXiv.org
Additional Information
This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/1108.0199