Gradient estimate on convex domains and applications

Feng Yu Wang*, Lixin Yan

*Corresponding author for this work

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    By solving the Skorokhod equation for reflecting diffusion processes on a convex domain, gradient estimates for the associated Neumann semigroup are derived. As applications, functional/Harnack inequalities are established for the Neumann semigroup. When the domain is bounded, the gradient estimates are applied to the study of Riesz transforms and regularity of the inhomogeneous Neumann problems on convex domains.

    Original languageEnglish
    Pages (from-to)1067-1081
    Number of pages15
    JournalProceedings of the American Mathematical Society
    Volume141
    Issue number3
    DOIs
    Publication statusPublished - 2013

    Keywords

    • Gradient estimates for Neumann semigroup
    • Green operator
    • Hardy space
    • Neumann problem
    • Reflecting diffusion process

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