An L                         p                          -estimate for the stochastic heat equation on an angular domain in R                         2

Petru A. Cioica-Licht; Kyeong Hun Kim; Kijung Lee; Felix Lindner

doi:10.1007/s40072-017-0102-9

An L _p -estimate for the stochastic heat equation on an angular domain in R ²

Petru A. Cioica-Licht, Kyeong Hun Kim, Kijung Lee, Felix Lindner

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

8 Citations (Scopus)

Abstract

We prove a weighted L _p -estimate for the stochastic convolution associated with the stochastic heat equation with zero Dirichlet boundary condition on a planar angular domain Dκ0⊂R2 with angle κ∈ (0 , 2 π). Furthermore, we use this estimate to establish existence and uniqueness of a solution to the corresponding equation in suitable weighted L _p -Sobolev spaces. In order to capture the singular behaviour of the solution and its derivatives at the vertex, we use powers of the distance to the vertex as weight functions. The admissible range of weight parameters depends explicitly on the angle κ.

Original language	English
Pages (from-to)	45-72
Number of pages	28
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
Volume	6
Issue number	1
DOIs	https://doi.org/10.1007/s40072-017-0102-9
Publication status	Published - 2018 Mar 1

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.

Keywords

Angular domain
Corner singularity
Non-smooth domain
Stochastic heat equation
Stochastic partial differential equation
Weighted L -estimate
Weighted Sobolev regularity

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

Access to Document

10.1007/s40072-017-0102-9

Cite this

Cioica-Licht, P. A., Kim, K. H., Lee, K., & Lindner, F. (2018). An L _p -estimate for the stochastic heat equation on an angular domain in R ² Stochastics and Partial Differential Equations: Analysis and Computations, 6(1), 45-72. https://doi.org/10.1007/s40072-017-0102-9

An L _p -estimate for the stochastic heat equation on an angular domain in R ² . / Cioica-Licht, Petru A.; Kim, Kyeong Hun; Lee, Kijung et al.
In: Stochastics and Partial Differential Equations: Analysis and Computations, Vol. 6, No. 1, 01.03.2018, p. 45-72.

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

Cioica-Licht, PA, Kim, KH, Lee, K & Lindner, F 2018, ' An L _p -estimate for the stochastic heat equation on an angular domain in R ² ', Stochastics and Partial Differential Equations: Analysis and Computations, vol. 6, no. 1, pp. 45-72. https://doi.org/10.1007/s40072-017-0102-9

Cioica-Licht, Petru A. ; Kim, Kyeong Hun ; Lee, Kijung et al. / An L _p -estimate for the stochastic heat equation on an angular domain in R ² In: Stochastics and Partial Differential Equations: Analysis and Computations. 2018 ; Vol. 6, No. 1. pp. 45-72.

@article{99890298792f41bfaec945e6a437707b,

title = " An L p -estimate for the stochastic heat equation on an angular domain in R 2 ",

abstract = " We prove a weighted L p -estimate for the stochastic convolution associated with the stochastic heat equation with zero Dirichlet boundary condition on a planar angular domain Dκ0⊂R2 with angle κ∈ (0 , 2 π). Furthermore, we use this estimate to establish existence and uniqueness of a solution to the corresponding equation in suitable weighted L p -Sobolev spaces. In order to capture the singular behaviour of the solution and its derivatives at the vertex, we use powers of the distance to the vertex as weight functions. The admissible range of weight parameters depends explicitly on the angle κ.",

keywords = "Angular domain, Corner singularity, Non-smooth domain, Stochastic heat equation, Stochastic partial differential equation, Weighted L -estimate, Weighted Sobolev regularity",

author = "Cioica-Licht, {Petru A.} and Kim, {Kyeong Hun} and Kijung Lee and Felix Lindner",

note = "Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media, LLC.",

year = "2018",

month = mar,

day = "1",

doi = "10.1007/s40072-017-0102-9",

language = "English",

volume = "6",

pages = "45--72",

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

issn = "2194-0401",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - An L p -estimate for the stochastic heat equation on an angular domain in R 2

AU - Cioica-Licht, Petru A.

AU - Kim, Kyeong Hun

AU - Lee, Kijung

AU - Lindner, Felix

PY - 2018/3/1

Y1 - 2018/3/1

N2 - We prove a weighted L p -estimate for the stochastic convolution associated with the stochastic heat equation with zero Dirichlet boundary condition on a planar angular domain Dκ0⊂R2 with angle κ∈ (0 , 2 π). Furthermore, we use this estimate to establish existence and uniqueness of a solution to the corresponding equation in suitable weighted L p -Sobolev spaces. In order to capture the singular behaviour of the solution and its derivatives at the vertex, we use powers of the distance to the vertex as weight functions. The admissible range of weight parameters depends explicitly on the angle κ.

AB - We prove a weighted L p -estimate for the stochastic convolution associated with the stochastic heat equation with zero Dirichlet boundary condition on a planar angular domain Dκ0⊂R2 with angle κ∈ (0 , 2 π). Furthermore, we use this estimate to establish existence and uniqueness of a solution to the corresponding equation in suitable weighted L p -Sobolev spaces. In order to capture the singular behaviour of the solution and its derivatives at the vertex, we use powers of the distance to the vertex as weight functions. The admissible range of weight parameters depends explicitly on the angle κ.

KW - Angular domain

KW - Corner singularity

KW - Non-smooth domain

KW - Stochastic heat equation

KW - Stochastic partial differential equation

KW - Weighted L -estimate

KW - Weighted Sobolev regularity

UR - http://www.scopus.com/inward/record.url?scp=85061707432&partnerID=8YFLogxK

U2 - 10.1007/s40072-017-0102-9

DO - 10.1007/s40072-017-0102-9

M3 - Article

AN - SCOPUS:85061707432

SN - 2194-0401

VL - 6

SP - 45

EP - 72

JO - Stochastics and Partial Differential Equations: Analysis and Computations

JF - Stochastics and Partial Differential Equations: Analysis and Computations

IS - 1

ER -