Elliptic equations for measures on infinite dimensional spaces and applications (Q5952003)

A new concept of weak elliptic equations for measures on infinitely dimensional spaces is considered. Applying a suitably extended Lyapunov functions technique the authors derive a priori estimates for the solutions of such equations and prove new existence results. The results are applied to stochastic Burgers reaction-diffusion and Navier-Stokes equations. Moment estimates for Gibbs distributions and existence results for a wide class of models are also obtained.