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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 \(\widetilde{\mathfrak {H}}_{p, \theta }^{\gamma }(S, T)\) 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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Acknowledgements

The authors would like to thank the anonymous referee for careful reading of the manuscript and helpful comments.

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  1. Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, Republic of Korea

    Doyoon Kim, Kyeong-Hun Kim & Kwan Woo

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  1. Doyoon Kim
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  3. Kwan Woo
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Correspondence to Kwan Woo.

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D. Kim and K. Woo were supported by the National Research Foundation of Korea (NRF) funded by the Korea government (MSIT) (2019R1A2C1084683).

K.-H. Kim was supported by the National Research Foundation of Korea (NRF) funded by the Korea government (MSIT) (2020R1A2C1A01003354).

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Kim, D., Kim, KH. & Woo, K. Trace theorem and non-zero boundary value problem for parabolic equations in weighted Sobolev spaces. Stoch PDE: Anal Comp 12, 134–172 (2024). https://doi.org/10.1007/s40072-022-00279-1

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  • DOI: https://doi.org/10.1007/s40072-022-00279-1

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