Trace theorem and non-zero boundary value problem for parabolic equations in weighted Sobolev spaces
Stochastics and Partial Differential Equations: Analysis and Computations(2024)
摘要
We present weighted Sobolev spaces ℌ_p, θ^γ(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.
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关键词
Weighted Sobolev spaces,Traces,Parabolic equations,Non-zero boundary value conditions
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