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

Bibliographical note

Funding Information:
Received October 20, 2017; Revised February 1, 2018; Accepted March 16, 2018. 2010 Mathematics Subject Classification. 58J05, 31B05. Key words and phrases. A-harmonic function, end, p-parabolicity, uniqueness. 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).

Publisher Copyright:
© 2018 Korean Mathematical Society.

Keywords

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

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