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
JournalStochastics and Partial Differential Equations: Analysis and Computations
DOIs
Publication statusAccepted/In press - 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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