Elliptic and parabolic equations for measures

V. I. Bogachev   ; N. V. Krylov   ; M. Röckner

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 64 (2009) no. 6, pp. 973-1078

Résumé

This article gives a detailed account of recent investigations of weak elliptic and parabolic equations for measures with unbounded and possibly singular coefficients. The existence and differentiability of densities are studied, and lower and upper bounds for them are discussed. Semigroups associated with second-order elliptic operators acting in $L^p$-spaces with respect to infinitesimally invariant measures are investigated. Bibliography: 181 titles.

Détail

Keywords: stationary distribution of a diffusion process, transition probability.
Mots-clés : elliptic equation, parabolic equation

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