Global Lorentz estimates for nonlinear parabolic equations on nonsmooth domains

The Anh Bui, Xuan Thinh Duong*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    Consider the nonlinear parabolic equation in the form ut − diva(Du, x, t) = div (|F|p−2F) in Ω × (0, T ), where T > 0 and Ω is a Reifenberg domain. We suppose that the nonlinearity a(ξ, x, t) has a small BMO norm with respect to x and is merely measurable and bounded with respect to the time variable t. In this paper, we prove the global Calderón-Zygmund estimates for the weak solution to this parabolic problem in the setting of Lorentz spaces which includes the estimates in Lebesgue spaces. Our global Calderón-Zygmund estimates extend certain previous results to equations with less regularity assumptions on the nonlinearity a(ξ, x, t) and to more general setting of Lorentz spaces.

    Original languageEnglish
    Article number47
    Pages (from-to)1-24
    Number of pages24
    JournalCalculus of Variations and Partial Differential Equations
    Volume56
    Issue number2
    DOIs
    Publication statusPublished - 2017

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