Trace theorem and non-zero boundary value problem for parabolic equations in weighted Sobolev spaces

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    Abstract

    We present weighted Sobolev spaces H~p,θγ(S,T) and prove a trace theorem for the spaces. As an application, we discuss non-zero boundary value problems for parabolic equations. The weighted parabolic Sobolev spaces we consider are designed, in particular, for the regularity theory of stochastic partial differential equations on bounded domains.

    Original languageEnglish
    Pages (from-to)134-172
    Number of pages39
    JournalStochastics and Partial Differential Equations: Analysis and Computations
    Volume12
    Issue number1
    DOIs
    Publication statusPublished - 2024 Mar

    Bibliographical note

    Publisher Copyright:
    © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022.

    Keywords

    • Non-zero boundary value conditions
    • Parabolic equations
    • Traces
    • Weighted Sobolev spaces

    ASJC Scopus subject areas

    • Statistics and Probability
    • Modelling and Simulation
    • Applied Mathematics

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