Trace theorem and non-zero boundary value problem for parabolic equations in weighted Sobolev spaces
arXiv:2105.05131
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.