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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Cioica-Licht, Petru A.¹  Kim, Kyeong-Hun²  Lee, Kijung³ 

[1] Univ Otago, Dept Math & Stat, POB 56, Dunedin 9054, New Zealand

[2] Korea Univ, Dept Math, Anam Ro 145, Seoul 02841, South Korea

[3] Ajou Univ, Dept Math, Worldcup Ro 206, Suwon 16499, South Korea

关键词: Stochastic partial differential equation;    Stochastic heat equation;    Weighted L-p-estimate;    Angular domain;    Polygonal domain;    Corner singularity;   

DOI  :  10.1016/j.jde.2019.06.027

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free