The Hopf-Laplace equation: Harmonicity and regularity

Jan Cristina; Tadeusz Iwaniec; Leonid V. Kovalev; Jani Onninen

The Hopf-Laplace equation: Harmonicity and regularity

Jan Cristina, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

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 mappings which are neither harmonic nor homeomorphisms. We prove that such mappings are harmonic outside of a singular set with small image. On the singular set they are locally Lipschitz, but not necessarily differentiable.

Original language	English (US)
Pages (from-to)	1145-1187
Number of pages	43
Journal	Annali della Scuola normale superiore di Pisa - Classe di scienze
Volume	13
Issue number	4
State	Published - 2014

ASJC Scopus subject areas

Theoretical Computer Science
Mathematics (miscellaneous)

Cite this

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AB - 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 mappings which are neither harmonic nor homeomorphisms. We prove that such mappings are harmonic outside of a singular set with small image. On the singular set they are locally Lipschitz, but not necessarily differentiable.

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The Hopf-Laplace equation: Harmonicity and regularity

Abstract

ASJC Scopus subject areas

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