Harnack inequality and applications for stochastic generalized porous media equations. (English) Zbl 1129.60060

Summary: 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 \(L^p\)-norm of the density as well as hypercontractivity, ultracontractivity and compactness of the corresponding semigroup are derived.


60H15 Stochastic partial differential equations (aspects of stochastic analysis)
76S05 Flows in porous media; filtration; seepage
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