Linear Stochastic Parabolic Equations , Degenerating on the Boundary of a Domain

@inproceedings{LototskyLinearSP,
title={Linear Stochastic Parabolic Equations , Degenerating on the Boundary of a Domain},
author={Sergey V. Lototsky}
}

A class of linear degenerate second-order parabolic equations is considered in arbitrary domains. It is shown that these equations are solvable using special weighted Sobolev spaces in essentially the same way as the non-degenerate equations in R d are solved using the usual Sobolev spaces. The main advantages of this Sobolev-space approach are less restrictive conditions on the coefficients of the equation and near-optimal space-time regularity of the solution. Unlike previous works on… CONTINUE READING