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

Research output: Contribution to journalArticlepeer-review

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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