Hölder continuity and bounds for fundamental solutions to nondivergence form parabolic equations

Seiichiro Kusuoka

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)1-32
    Number of pages32
    JournalAnalysis and PDE
    Volume8
    Issue number1
    DOIs
    Publication statusPublished - 2015

    Keywords

    • Coupling method
    • Diffusion
    • Fundamental solution
    • Gaussian estimate
    • Hölder continuity
    • Parabolic partial differential equation
    • Stochastic differential equation

    ASJC Scopus subject areas

    • Analysis
    • Numerical Analysis
    • Applied Mathematics

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