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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.

MSC:

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