The weak maximum principle for second-order elliptic and parabolic conormal derivative problems

Doyoon Kim, Seungjin Ryu

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)

    Abstract

    We prove the weak maximum principle for second-order elliptic and parabolic equations in divergence form with the conormal derivative boundary conditions when the lower-order coefficients are unbounded and domains are beyond Lipschitz boundary regularity. In the elliptic case we consider John domains and lower-order coefficients in Ln spaces (ai, bi ∈ Lq, c ∈ Lq/2, q = n if n ≥ 3 and q > 2 if n = 2). For the parabolic case, the lower-order coefficients ai, bi, and c belong to Lq,r spaces (ai, bi, |c|1/2 ∈ Lq,r with n/q + 2/r ≤ 1), q ∈ (n, ∞], r ∈ [2, ∞], n ≥ 2. We also consider coefficients in Ln,∞ with a smallness condition for parabolic equations.

    Original languageEnglish
    Pages (from-to)493-510
    Number of pages18
    JournalCommunications on Pure and Applied Analysis
    Volume19
    Issue number1
    DOIs
    Publication statusPublished - 2020

    Bibliographical note

    Funding Information:
    2000 Mathematics Subject Classification. 35B50, 35K20, 35J25. Key words and phrases. Weak maximum principle, conormal derivative boundary condition, John domain. S. Ryu was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2017R1C1B1010966). D. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A1B03934369).

    Publisher Copyright:
    © 2020 American Institute of Mathematical Sciences. All rights reserved.

    Keywords

    • Conormal derivative boundary condition
    • John domain
    • Weak maximum principle

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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