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Hölder continuity and
bounds for fundamental solutions to nondivergence form
parabolic equations
Seiichiro Kusuoka |
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Vol. 8 (2015), No. 1, 1–32
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Abstract |
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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. |
Keywords
parabolic partial differential equation, diffusion,
fundamental solution, Hölder continuity, Gaussian estimate,
stochastic differential equation, coupling method
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Mathematical Subject Classification 2010
Primary: 35B65, 35K10, 60H30
Secondary: 60H10, 60J60
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Milestones
Received: 16 October 2013
Revised: 6 November 2014
Accepted: 21 December 2014
Published: 15 April 2015
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Authors |
| Seiichiro Kusuoka | |
| Graduate School of Science Tohoku University 6-3 Aramaki Aza-Aoba Aoba-ku Sendai 980-8578 Japan |
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