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.
"Harnack inequality and applications for stochastic generalized porous media equations." Ann. Probab. 35 (4) 1333 - 1350, July 2007. https://doi.org/10.1214/009117906000001204