We establish existence, uniqueness and higher order weighted Lp-Sobolev regularity for the stochastic heat equation with zero Dirichlet boundary condition on angular domains and on polygonal domains in R2. 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.
The first named author has been partially supported by the Marsden Fund Council from Government funding, administered by the Royal Society of New Zealand, and by a University of Otago Research Grant (114023.01.R.FO). The research of the second and third author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1B03033255) and (NRF-2013R1A1A2060996), respectively. The authors would like to thank Felix Lindner for his contribution at an early stage of this manuscript.☆ The first named author has been partially supported by the Marsden Fund Council from Government funding, administered by the Royal Society of New Zealand, and by a University of Otago Research Grant ( 114023.01.R.FO). The research of the second and third author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2017R1D1A1B03033255) and ( NRF-2013R1A1A2060996), respectively. The authors would like to thank Felix Lindner for his contribution at an early stage of this manuscript.The first named author has been partially supported by the Marsden Fund Council from Government funding, administered by the Royal Society of New Zealand, and by a University of Otago Research Grant (114023.01.R.FO). The research of the second and third author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1B03033255) and (NRF-2013R1A1A2060996), respectively. The authors would like to thank Felix Lindner for his contribution at an early stage of this manuscript.
