Uniqueness of solutions of a certain nonlinear elliptic equation on riemannian manifolds

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Abstract

In this paper, we prove that if every bounded A-harmonic function on a complete Riemannian manifold M is asymptotically constant at infinity of p-nonparabolic ends of M, then each bounded A-harmonic function is uniquely determined by the values at infinity of p-nonparabolic ends of M, where A is a nonlinear elliptic operator of type p on M. Furthermore, in this case, every bounded A-harmonic function on M has finite energy.

Original languageEnglish
Pages (from-to)1577-1586
Number of pages10
JournalBulletin of the Korean Mathematical Society
Volume55
Issue number5
DOIs
StatePublished - 2018

Keywords

  • A-harmonic function
  • End
  • p-parabolicity
  • Uniqueness

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