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Heat kernels and regularity for rough metrics on smooth manifolds
Author(s) -
Bandara Lashi,
Bryan Paul
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800459
Subject(s) - mathematics , heat kernel , divergence (linguistics) , sobolev space , harnack's principle , bounded function , harnack's inequality , hölder condition , heat equation , space (punctuation) , pure mathematics , mathematical analysis , philosophy , linguistics
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.