Asymptotic Boundary Value Problem of Harmonic Maps via Harmonic Boundary

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Abstract

We prove that given any continuous data f on the harmonic boundary of a complete Riemannian manifold with image within a ball in the normal range, there exists a harmonic map from the manifold into the ball taking the same boundary value at each harmonic boundary point as that of f.

Original languageEnglish
Pages (from-to)463-468
Number of pages6
JournalPotential Analysis
Volume41
Issue number2
DOIs
StatePublished - Jun 2014

Bibliographical note

Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(2012006926).

Keywords

  • Asymptotic boundary value problem
  • Harmonic boundary
  • Harmonic map

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