### 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 | |

Publication status | Published - 2018 Mar 1 |

### Fingerprint

### 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

### Cite this

_{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; Lindner, Felix.

Research output: Contribution to journal › Article

_{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

_{p}-estimate for the stochastic heat equation on an angular domain in R

^{2}Stochastics and Partial Differential Equations: Analysis and Computations. 2018 Mar 1;6(1):45-72. https://doi.org/10.1007/s40072-017-0102-9

}

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

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

U2 - 10.1007/s40072-017-0102-9

DO - 10.1007/s40072-017-0102-9

M3 - Article

AN - SCOPUS:85061707432

VL - 6

SP - 45

EP - 72

JO - Stochastics and Partial Differential Equations: Analysis and Computations

JF - Stochastics and Partial Differential Equations: Analysis and Computations

SN - 2194-0401

IS - 1

ER -