Document Type

Article

Date

11-26-2010

Embargo Period

11-14-2011

Disciplines

Mathematics

Description/Abstract

The central theme in this paper is the Hopf-Laplace equation, which represents stationary solutions with respect to the inner variation of the Dirichlet integral. Among such solutions are harmonic maps. Nevertheless, minimization of the Dirichlet energy among homeomorphisms often leads to nonharmonic solutions. We investigate the Hopf-Laplace equation for a certain class of topologically well behaved mappings which are almost homeomorphisms, called Hopf deformations. We establish Lipschitz continuity of Hopf deformations, the best possible regularity one can get. Thus in particular we show that the minimal-energy deformations are Lipschitz continuous, a result of considerable interest in the theory of minimal surfaces, calculus of variations, and PDEs, with potential applications to elastic plates.

Additional Information

This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/1011.5934

Source

Harvested from arXiv.org

Creative Commons License


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

Included in

Mathematics Commons

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