Dirichlet Problem for Stochastic Parabolic Equations in Smooth Domains
نویسنده
چکیده
A second-order stochastic parabolic equation with zero Dirichlet boundary conditions is considered in a sufficiently smooth bounded domain. Existence, uniqueness, and regularity of the solution are established without assuming any compatibility relations. To control the solution near the boundary of the region, special Sobolev-type spaces with weights are introduced. To illustrate the results, two examples are considered: general linear equation with finite-dimensional noise and equation on a line segment, driven by space-time white noise. Published in Stochastics and Stochastics Reports, Vol. 68, pp. 145–175, 2000.
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تاریخ انتشار 1999