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 Lp-spaces with respect to infinitesimally invariant measures are investigated.
- Elliptic equation
- Parabolic equation
- Stationary distribution of a diffusion process
- Transition probability