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arXiv · 2105.05131

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

Doyoon Kim·Kyeong-Hun Kim·Kwan Woo
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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.

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Doyoon Kim, Kyeong-Hun Kim, Kwan Woo. 2021-05-11. Trace theorem and non-zero boundary value problem for parabolic equations in weighted Sobolev spaces. https://arxiv.org/abs/2105.05131

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