Harnack inequality and applications for stochastic generalized porous media equations

Details Harnack inequality and applications for stochastic generalized porous media equations Harnack inequality and applications for stochastic generalized porous media equations

2007-08-13

arxiv.org/abs/0708.1671v1

Annals of Probability 2007, Vol. 35, No. 4, 1333-1350

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000001204 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000001204

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.

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