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Heat kernels and regularity for rough metrics on smooth manifolds

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  • Lashi Bandara
  • Paul Bryan

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.

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  • Lashi Bandara & Paul Bryan, 2020. "Heat kernels and regularity for rough metrics on smooth manifolds," Mathematische Nachrichten, Wiley Blackwell, vol. 293(12), pages 2255-2270, December.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:12:p:2255-2270
    DOI: 10.1002/mana.201800459
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    References listed on IDEAS

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    1. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, February.
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