Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of "Noises"

The concept of "white noise", initially established in fnite-dimentional spaces, is transferred to infinite-dimentional case. The goal of this transition is to devolop the theory of stochastic Sobolev type equations and to elaborate applications of practical interest. To reach this goal the Nelson-Gliklikh derivative is introduced and the spaces of "noises" are developed. The Sobolev type equations with relatively sectorial operators are considered in the spaces of differentiable "noises". The existance and uniqueness of classical solutions are proved. The stocastic Dzektser equation in a bounded domain with homogeneous boundary condition and the weakened Showalter-Sidorov initial condition is considered as an application.