Document Type

Article

Date

7-31-2011

Embargo Period

11-14-2011

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.

Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/1108.0199

Source

Harvested from arXiv.org

Included in

Mathematics Commons

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