Once again on evolution equations with monotone operators in Hilbert spaces and applications

TL;DR

This paper investigates the existence, uniqueness, and stability of solutions to linear stochastic evolution equations, applying these results to solve second order stochastic PDEs with singular coefficients in an $L_p$-setting.

Contribution

It provides new theorems on solvability of linear second order stochastic PDEs with singular coefficients using evolution equations with monotone operators.

Findings

Proved existence and uniqueness of solutions for linear stochastic evolution equations.

Established stability results for these solutions.

Applied findings to solve stochastic PDEs with singular lower order coefficients.

Abstract

Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations in $L_{p}$-setting with singular lower order coefficients.