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^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	134-172
Number of pages	39
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
Volume	12
Issue number	1
DOIs	https://doi.org/10.1007/s40072-022-00279-1
Publication status	Published - 2024 Mar

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 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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abstract = "We present weighted Sobolev spaces H\textasciitilde{}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",

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AU - Woo, Kwan

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022.

PY - 2024/3

Y1 - 2024/3

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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M3 - Article

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JO - Stochastics and Partial Differential Equations: Analysis and Computations

JF - Stochastics and Partial Differential Equations: Analysis and Computations

IS - 1

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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