#### Document Type

Article

#### Date

8-3-2010

#### Embargo Period

11-14-2011

#### Keywords

tbd

#### Disciplines

Mathematics

#### Description/Abstract

The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy. Specifically, among all homeomorphisms f : omega -> omega* between bounded doubly connected domains such that Mod (omega) < Mod (omega*) there exists, unique up to conformal authomorphisms of omega, 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.

#### Recommended Citation

Iwaniec, Tadeusz; Koh, Ngin-Tee; Kovalev, Leonid V.; and Onninen, Jani, "Existence of Energy-Minimal Diffeomorphisms Between Doubly Connected Domains" (2010). *Mathematics Faculty Scholarship.* Paper 52.

http://surface.syr.edu/mat/52

#### Source

Harvested from arXiv.org

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.

## Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/1008.0652