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Heat kernels and regularity for rough metrics on smooth manifolds

Version 2 2024-06-03, 01:33
Version 1 2023-11-03, 03:55
journal contribution
posted on 2024-06-03, 01:33 authored by Lashi BandaraLashi Bandara, P Bryan
AbstractWe 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.

History

Journal

Mathematische Nachrichten

Volume

293

Pagination

2255-2270

Location

London, Eng.

ISSN

0025-584X

eISSN

1522-2616

Language

English

Publication classification

C1.1 Refereed article in a scholarly journal

Issue

12

Publisher

Wiley