#### 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 W^{1,2} extends to a continuous map between closed domains. We prove that there exist homeomorphisms between closed domains which converge to h uniformly and in W^{1,2}. 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 Faculty Scholarship.* Paper 56.

http://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