On divergence form SPDEs with VMO coefficients in a half space

TL;DR

This paper extends solvability results for divergence form stochastic partial differential equations in a half-space to include equations with discontinuous coefficients, broadening the class of solvable SPDEs.

Contribution

It introduces methods to handle SPDEs with VMO coefficients in divergence form within a half-space, advancing the theory for equations with discontinuous coefficients.

Findings

Established solvability in Sobolev spaces for SPDEs with VMO coefficients

Extended known results to equations with discontinuous coefficients

Provided new techniques for SPDEs in divergence form in a half-space

Abstract

We extend several known results on solvability in the Sobolev spaces $W^{1}_{p}$, $p\in[2,\infty)$, of SPDEs in divergence form in $\bR^{d}_{+}$ to equations having coefficients which are discontinuous in the space variable.