An $L_p$-estimate for the stochastic heat equation on angular domains in $\mathbb{R}^2$ with mixed weights

Petru A. Cioica-Licht

Published 2020-03-08Version 1

We establish a refined $L_p$-estimate ($p\geq 2$) for the stochastic heat equation on angular domains in $\mathbb{R}^2$ 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.