TY - JOUR AB - A new concept of a weak elliptic equation for probability distributions on infinite dimensional spaces is introduced. A suitable notion of a Lyapunov function is defined for weak elliptic equations. Sufficient conditions in terms of Lyapunov functions are given for the existence of solutions for weak elliptic equations. Applications to Gibbs measures are discussed. (C) 1999 Academie des sciences/Editions scientifiques et medicales Elsevier SAS. AU - Bogachev, Vladimir AU - Röckner, Michael ID - 1621467 IS - 8 JF - Comptes Rendus de l'Académie des Sciences - Series I - Mathematics SN - 0764-4442 TI - Elliptic equations for infinite dimensional probability distributions and Lyapunov functions VL - 329 ER -