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

Doyoon Kim; Kyeong Hun Kim; Kwan Woo

doi:10.1007/s40072-022-00279-1

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

Doyoon Kim, Kyeong Hun Kim, Kwan Woo

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We present weighted Sobolev spaces H~p,θγ(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.

Original language	English
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
DOIs	https://doi.org/10.1007/s40072-022-00279-1
Publication status	Accepted/In press - 2022

Keywords

Non-zero boundary value conditions
Parabolic equations
Traces
Weighted Sobolev spaces

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1007/s40072-022-00279-1

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

abstract = "We present weighted Sobolev spaces H~p,θγ(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.",

keywords = "Non-zero boundary value conditions, Parabolic equations, Traces, Weighted Sobolev spaces",

author = "Doyoon Kim and Kim, {Kyeong Hun} and Kwan Woo",

note = "Funding Information: D. Kim and K. Woo were supported by the National Research Foundation of Korea (NRF) funded by the Korea government (MSIT) (2019R1A2C1084683). Funding Information: K.-H. Kim was supported by the National Research Foundation of Korea (NRF) funded by the Korea government (MSIT) (2020R1A2C1A01003354). Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2022",

doi = "10.1007/s40072-022-00279-1",

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journal = "Stochastics and Partial Differential Equations: Analysis and Computations",

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AU - Kim, Doyoon

AU - Kim, Kyeong Hun

AU - Woo, Kwan

N1 - Funding Information: D. Kim and K. Woo were supported by the National Research Foundation of Korea (NRF) funded by the Korea government (MSIT) (2019R1A2C1084683). Funding Information: K.-H. Kim was supported by the National Research Foundation of Korea (NRF) funded by the Korea government (MSIT) (2020R1A2C1A01003354). Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022

Y1 - 2022

N2 - We present weighted Sobolev spaces H~p,θγ(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.

AB - We present weighted Sobolev spaces H~p,θγ(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.

KW - Non-zero boundary value conditions

KW - Parabolic equations

KW - Traces

KW - Weighted Sobolev spaces

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DO - 10.1007/s40072-022-00279-1

M3 - Article

AN - SCOPUS:85142218487

SN - 2194-0401

JO - Stochastics and Partial Differential Equations: Analysis and Computations

JF - Stochastics and Partial Differential Equations: Analysis and Computations

ER -

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

Abstract

Keywords

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