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

TL;DR

This paper develops weighted Sobolev spaces and proves a trace theorem, applying these results to non-zero boundary value problems for parabolic equations, with implications for stochastic PDE regularity.

Contribution

It introduces weighted Sobolev spaces tailored for parabolic PDEs and establishes a trace theorem, advancing boundary value problem analysis in this context.

Findings

Proved a trace theorem for weighted Sobolev spaces.

Applied the theorem to non-zero boundary value problems.

Enhanced understanding of regularity for stochastic PDEs.

Abstract

We present weighted Sobolev spaces 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.