Heat kernels and regularity for rough metrics on smooth manifolds

Lashi Bandara and Paul Bryan

Mathematische Nachrichten, 2020, vol. 293, issue 12, 2255-2270

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.

Date: 2020
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https://doi.org/10.1002/mana.201800459

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