Preprint
An Lp-theory for the stochastic heat equation on angular domains in R2 with mixed weights
Publication Details
Authors: | Cioica-Licht, P. |
Publication year: | 2020 |
Journal: | arXiv Preprint |
Pages range : | 1-20 |
Journal acronym: | arXiv |
DOI-Link der Erstveröffentlichung: |
Abstract
We establish a refined $L_p$-estimate ({\$}p$\backslash$geq 2{\$}) for the stochastic heat equation on angular domains in {\$}\mathbbR{\^{}}}2{\$} with mixed weights based on both, the distance to the boundary and the distance to the vertex. This way we can capture both causes for singularities of the solution: the incompatibility of noise and boundary condition on the one hand and the influence of boundary singularities (here, the vertex) on the other hand. Higher order $L_p$-Sobolev regularity with mixed weights is also established.
We establish a refined $L_p$-estimate ({\$}p$\backslash$geq 2{\$}) for the stochastic heat equation on angular domains in {\$}\mathbbR{\^{}}}2{\$} with mixed weights based on both, the distance to the boundary and the distance to the vertex. This way we can capture both causes for singularities of the solution: the incompatibility of noise and boundary condition on the one hand and the influence of boundary singularities (here, the vertex) on the other hand. Higher order $L_p$-Sobolev regularity with mixed weights is also established.
