The Hopf-Laplace equation: Harmonicity and regularity

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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 languageEnglish (US)
Pages (from-to)1145-1187
Number of pages43
JournalAnnali della Scuola normale superiore di Pisa - Classe di scienze
Issue number4
StatePublished - 2014

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)


Dive into the research topics of 'The Hopf-Laplace equation: Harmonicity and regularity'. Together they form a unique fingerprint.

Cite this