Heat kernels and regularity for rough metrics on smooth manifolds

Lashi Bandara, Paul Bryan*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Hölder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.

Original languageEnglish
Pages (from-to)2255-2270
Number of pages16
JournalMathematische Nachrichten
Volume293
Issue number12
DOIs
Publication statusPublished - Dec 2020

Keywords

  • heat kernel
  • parabolic Harnack estimate
  • rough metrics

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