On divergence form SPDEs with VMO coefficients

TL;DR

This paper investigates the solvability of divergence form stochastic partial differential equations in Sobolev spaces, providing new theoretical insights into their solutions under certain coefficient conditions.

Contribution

It offers novel results on the existence and uniqueness of solutions for SPDEs with VMO coefficients in divergence form, expanding the theoretical understanding.

Findings

Established solvability conditions in Sobolev spaces

Proved existence and uniqueness of solutions

Extended results to equations with VMO coefficients

Abstract

We present several results on solvability in Sobolev spaces $W^{1}_{p}$ of SPDEs in divergence form in the whole space.