On the regularity of the stochastic heat equation on polygonal domains in R-2
- Authors
- Cioica-Licht, Petru A.; Kim, Kyeong-Hun; Lee, Kijung
- Issue Date
- 15-11월-2019
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Stochastic partial differential equation; Stochastic heat equation; Weighted L-p-estimate; Angular domain; Polygonal domain; Corner singularity
- Citation
- JOURNAL OF DIFFERENTIAL EQUATIONS, v.267, no.11, pp.6447 - 6479
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF DIFFERENTIAL EQUATIONS
- Volume
- 267
- Number
- 11
- Start Page
- 6447
- End Page
- 6479
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/61576
- DOI
- 10.1016/j.jde.2019.06.027
- ISSN
- 0022-0396
- 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. (C) 2019 Elsevier Inc. All rights reserved.
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