Heat kernels and regularity for rough metrics on smooth manifolds

2017/12/26 by Bandara, Lashi, Bryan, Paul · 1 citation
#35K10 #58B20 #58J35 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1712.09287

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.

Cited by

• The space of rough Riemannian metrics

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