Document Type
Article
Date
11-26-2010
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.
Recommended Citation
Cristina, Jan; Iwaniec, Tadeusz; Kovalev, Leonid V.; and Onninen, Jani, "The Hopf-Laplace Equation" (2010). Mathematics - All Scholarship. 54.
https://surface.syr.edu/mat/54
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/1011.5934