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2015 Hölder continuity and bounds for fundamental solutions to nondivergence form parabolic equations
Seiichiro Kusuoka
Anal. PDE 8(1): 1-32 (2015). DOI: 10.2140/apde.2015.8.1

Abstract

We consider nondegenerate second-order parabolic partial differential equations in nondivergence form with bounded measurable coefficients (not necessary continuous). Under certain assumptions weaker than the Hölder continuity of the coefficients, we obtain Gaussian bounds and Hölder continuity of the fundamental solution with respect to the initial point. Our proofs employ pinned diffusion processes for the probabilistic representation of fundamental solutions and the coupling method.

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Seiichiro Kusuoka. "Hölder continuity and bounds for fundamental solutions to nondivergence form parabolic equations." Anal. PDE 8 (1) 1 - 32, 2015. https://doi.org/10.2140/apde.2015.8.1

Information

Received: 16 October 2013; Revised: 6 November 2014; Accepted: 21 December 2014; Published: 2015
First available in Project Euclid: 28 November 2017

zbMATH: 1316.35064
MathSciNet: MR3336920
Digital Object Identifier: 10.2140/apde.2015.8.1

Subjects:
Primary: 35B65, 35K10, 60H30
Secondary: 60H10, 60J60

Rights: Copyright © 2015 Mathematical Sciences Publishers

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