Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces

Kazuhiro Kuwae, Yoshiroh Machigashira, Takashi Shioya

Research output: Contribution to journalArticlepeer-review

70 Citations (Scopus)

Abstract

We prove the compactness of the imbedding of the Sobolev space W1,20 (Ω) into L2 (Ω) for any relatively compact open subset Ω of an Alexandrov space. As a corollary, the generator induced from the Dirichlet (energy) form has discrete spectrum. The generator can be approximated by the Laplacian induced from the DC-structure on the Alexandrov space. We also prove the existence of the locally Hölder continuous heat kernel.

Original languageEnglish
Pages (from-to)269-316
Number of pages48
JournalMathematische Zeitschrift
Volume238
Issue number2
DOIs
Publication statusPublished - 2001 Oct 1

ASJC Scopus subject areas

  • Mathematics(all)

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