### Abstract

We establish existence, uniqueness and higher order weighted L_{p}-Sobolev regularity for the stochastic heat equation with zero Dirichlet boundary condition on angular domains and on polygonal domains in R^{2}. We use a system of mixed weights consisting of appropriate powers of the distance to the vertexes and of the distance to the boundary to measure the regularity with respect to the space variable. In this way we can capture the influence of both main sources for singularities: the incompatibility between noise and boundary condition on the one hand and the singularities of the boundary on the other hand. The range of admissible powers of the distance to the vertexes is described in terms of the maximal interior angle and is sharp.

Original language | English |
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Journal | Journal of Differential Equations |

DOIs | |

Publication status | Published - 2019 Jan 1 |

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### Keywords

- Angular domain
- Corner singularity
- Polygonal domain
- Stochastic heat equation
- Stochastic partial differential equation
- Weighted L-estimate

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

^{2}

*Journal of Differential Equations*. https://doi.org/10.1016/j.jde.2019.06.027

**On the regularity of the stochastic heat equation on polygonal domains in R ^{2} .** / Cioica-Licht, Petru A.; Kim, Kyeong Hun; Lee, Kijung.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On the regularity of the stochastic heat equation on polygonal domains in R2

AU - Cioica-Licht, Petru A.

AU - Kim, Kyeong Hun

AU - Lee, Kijung

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We establish existence, uniqueness and higher order weighted Lp-Sobolev regularity for the stochastic heat equation with zero Dirichlet boundary condition on angular domains and on polygonal domains in R2. We use a system of mixed weights consisting of appropriate powers of the distance to the vertexes and of the distance to the boundary to measure the regularity with respect to the space variable. In this way we can capture the influence of both main sources for singularities: the incompatibility between noise and boundary condition on the one hand and the singularities of the boundary on the other hand. The range of admissible powers of the distance to the vertexes is described in terms of the maximal interior angle and is sharp.

AB - We establish existence, uniqueness and higher order weighted Lp-Sobolev regularity for the stochastic heat equation with zero Dirichlet boundary condition on angular domains and on polygonal domains in R2. We use a system of mixed weights consisting of appropriate powers of the distance to the vertexes and of the distance to the boundary to measure the regularity with respect to the space variable. In this way we can capture the influence of both main sources for singularities: the incompatibility between noise and boundary condition on the one hand and the singularities of the boundary on the other hand. The range of admissible powers of the distance to the vertexes is described in terms of the maximal interior angle and is sharp.

KW - Angular domain

KW - Corner singularity

KW - Polygonal domain

KW - Stochastic heat equation

KW - Stochastic partial differential equation

KW - Weighted L-estimate

UR - http://www.scopus.com/inward/record.url?scp=85068448496&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068448496&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2019.06.027

DO - 10.1016/j.jde.2019.06.027

M3 - Article

AN - SCOPUS:85068448496

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

ER -