Elliptic Estimates Through Stochastic Analysis

Abstract

Variation of an ODE: linearized ODE determining the Jacobian ma­trix — The control map, its Jacobian — Jacobian of a stochastic flow — Higher derivatives of a stochastic flow — Itô functionals, their differentiability — Malliavin matrix of an Itô functional — Reduced variation of an Itô functional — Reduced vari­ation and regularity in the backward variables — Bismut’s identity — Hörmander’s hypoellipticity theorem.