An L-P-estimate for the stochastic heat equation on an angular domain in R-2
- Authors
- Cioica-Licht, Petru A.; Kim, Kyeong-Hun; Lee, Kijung; Lindner, Felix
- Issue Date
- 3월-2018
- Publisher
- SPRINGER
- Keywords
- Stochastic partial differential equation; Stochastic heat equation; Weighted L-p-estimate; Weighted Sobolev regularity; Angular domain; Non-smooth domain; Corner singularity
- Citation
- STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, v.6, no.1, pp.45 - 72
- Indexed
- SCOPUS
- Journal Title
- STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS
- Volume
- 6
- Number
- 1
- Start Page
- 45
- End Page
- 72
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/77248
- DOI
- 10.1007/s40072-017-0102-9
- ISSN
- 2194-0401
- 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 D-kappa 0 subset of R-2 with angle kappa(0) is an element of (0, 2 pi). 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 kappa(0) .
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Collections - College of Science > Department of Mathematics > 1. Journal Articles
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