A weighted L p-theory for parabolic PDEs with BMO coefficients on C 1-domains

Kyeong Hun Kim, Kijung Lee

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)

    Abstract

    In this paper we present a weighted L p-theory of second-order parabolic partial differential equations defined on C 1 domains. The leading coefficients are assumed to be measurable in time variable and have VMO (vanishing mean oscillation) or small BMO (bounded mean oscillation) with respect to space variables, and lower order coefficients are allowed to be unbounded and to blow up near the boundary. Our BMO condition is slightly relaxed than the others in the literature.

    Original languageEnglish
    Pages (from-to)368-407
    Number of pages40
    JournalJournal of Differential Equations
    Volume254
    Issue number2
    DOIs
    Publication statusPublished - 2013 Jan 15

    Bibliographical note

    Funding Information:
    E-mail addresses: [email protected] (K.-H. Kim), [email protected] (K. Lee). 1 The research of this author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0015961). 2 The research of this author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0005597).

    Keywords

    • BMO coefficients
    • L -theory
    • Parabolic equations
    • VMO coefficients
    • Weighted Sobolev spaces

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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