Global Marcinkiewicz estimates for nonlinear parabolic equations with nonsmooth coefficients

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    Abstract

    Consider the parabolic equation with measure data (Equation Presented) where Ω is a bounded domain in Rn, ΩT = Ω × (0, T), ∂pΩT = (∂Ω × (0, T))U (Ω × {0}), and μ is a signed Borel measure with finite total mass. Assume that the nonlinearity a satisfies a small BMO-seminorm condition, and Ω is a Reifenberg flat domain. This paper proves a global Marcinkiewicz estimate for the SOLA (Solution Obtained as Limits of Approximation) to the parabolic equation.

    Original languageEnglish
    Pages (from-to)881-916
    Number of pages36
    JournalAnnali della Scuola normale superiore di Pisa - Classe di scienze
    Volume18
    Issue number3
    DOIs
    Publication statusPublished - 1 Jan 2018

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