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- W2953133775 abstract "In this paper we study parabolic stochastic partial differential equations defined on arbitrary bounded domain $cO subset bR^d$ allowing Hardy inequality: $$ int_{cO}|rho^{-1}g|^2,dxleq Cint_{cO}|g_x|^2 dx, quad forall gin C^{infty}_0(cO), $$ where $rho(x)=text{dist}(x,partial cO)$. Existence and uniqueness results are given in weighted Sobolev spaces $frH^{gamma}_{p,theta}(cO,T)$, where $pin [2,infty)$, $gammain bR$ is the number of derivatives of solutions and $theta$ controls the boundary behavior of solutions. Furthermore several Holder estimates of the solutions are also obtained. It is allowed that the coefficients of the equations blow up near the boundary." @default.
- W2953133775 created "2019-06-27" @default.
- W2953133775 creator A5056956197 @default.
- W2953133775 date "2011-09-22" @default.
- W2953133775 modified "2023-09-24" @default.
- W2953133775 title "A weighted Sobolev space theory of parabolic stochastic PDEs on non-smooth domains" @default.
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- W2953133775 doi "https://doi.org/10.48550/arxiv.1109.4727" @default.
- W2953133775 hasPublicationYear "2011" @default.
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