On Bellman's equations with VMO coefficients

TL;DR

This paper proves the solvability of Bellman's equations with VMO coefficients in the whole space for certain Sobolev spaces, also discussing related parabolic equations.

Contribution

It establishes new solvability results for Bellman's equations with VMO coefficients in $W^{2}_{p}$ spaces, extending understanding in this area.

Findings

Solvability in $W^{2}_{p}$ for Bellman's equations with VMO coefficients

Extension to parabolic equations

Results applicable in the whole space $R^{d}$

Abstract

We present a result about solvability in $W^{2}_{p}$, $p>d$, in the whole space $\bR^{d}$ of Bellman's equations with VMO ``coefficients''. Parabolic equations are touched upon as well.