Harnack inequality and applications for stochastic generalized porous media equations

Abstract

By using coupling and Girsanov transformations, the dimension-free Harnack inequality and the strong Feller property are proved for transition semigroups of solutions to a class of stochastic generalized, porous media equations. As applications, explicit upper bounds of the Lp-norm of the density as well as hypercontractivity, ultracontractivity and compactness of the corresponding semigroup are derived. © Institute of Mathematical Statistics, 2007.