Uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators via p-harmonic boundary

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Abstract

We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.

Original languageEnglish
Pages (from-to)1025-1031
Number of pages7
JournalCommunications of the Korean Mathematical Society
Volume32
Issue number4
DOIs
StatePublished - 2017

Keywords

  • A-harmonic function
  • Boundary value problem
  • P-harmonic boundary

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