On divergence form SPDEs with growing coefficients in $W^{1}_{2}$ spaces without weights

TL;DR

This paper studies divergence form stochastic partial differential equations with unbounded coefficients, establishing existence and regularity of solutions in Sobolev spaces without weights.

Contribution

It provides new results on the solvability and regularity of divergence form SPDEs with growing coefficients in unweighted Sobolev spaces.

Findings

Existence of solutions in W^{1}_2 spaces without weights

Regularity results for solutions and their derivatives

Handling of unbounded coefficients in SPDEs

Abstract

We consider divergence form uniformly parabolic SPDEs with bounded and measurable leading coefficients and possibly growing lower-order coefficients in the deterministic part of the equations. We look for solutions which are summable to the second power with respect to the usual Lebesgue measure along with their first derivatives with respect to the spatial variable.