The Hopf-Laplace equation: harmonicity and regularity

• Jan Cristina ^[1] ; Tadeusz Iwaniec ^[2] ; Leonid V. Kovalev ^[2] ; Jani Onninen ^[2]
  1. [1] University of Helsinki

     University of Helsinki

     Helsinki, Finlandia

     
  2. [2] Syracuse University

     Syracuse University

     City of Syracuse, Estados Unidos

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 13, Nº 4, 2014, págs. 1145-1187
• Idioma: inglés
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• Resumen

  • 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