Essential self adjointness of Laplacians on Riemannian manifolds with fractal boundary

Jun Masamune

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

We study the problem of the essential self-adjointness of Laplacians on Riemannian manifolds. We show that a sufficient condition is if the boundary of a manifold M. by which we mean M̄\M, where M̄ is the metric completion of M, is almost polar set. Two other results concern special cases, when the boundary is some sort of fractal set or even a manifold. It is shown that the boundary is almost polar set in the cases under certain dimensional restrictions.

Original languageEnglish
Pages (from-to)749-757
Number of pages9
JournalCommunications in Partial Differential Equations
Volume24
Issue number3-4
DOIs
Publication statusPublished - 1999 Jan 1

Keywords

  • Essential self-adjointness
  • Fractals
  • Laplacians

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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