An L_p-theory for the stochastic heat equation on angular domains in ℝ² with mixed weights

2020/03/08 by Petru A. Cioica-Licht, Cioica-Licht, Petru A.
Economics, Econometrics and Finance · Mathematics · #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations #Stochastic processes and financial applications #math.AP #math.PR #msc:35K05 #msc:35R60 #msc:60H15

paper · pdf · doi:10.48550/arxiv.2003.03782

Version 1: $L_p$-estimates; New in Version 2: Weighted $L_p$-Sobolev regularity of arbitrary positive integer order

arxiv created 2020/03/22 · arxiv updated 2020/03/24

Abstract

We establish a refined L_p-estimate (p≥ 2) for the stochastic heat equation on angular domains in ℝ² 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.

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