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July 2007 Harnack inequality and applications for stochastic generalized porous media equations
Feng-Yu Wang
Ann. Probab. 35(4): 1333-1350 (July 2007). DOI: 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 Lp-norm of the density as well as hypercontractivity, ultracontractivity and compactness of the corresponding semigroup are derived.


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Feng-Yu Wang. "Harnack inequality and applications for stochastic generalized porous media equations." Ann. Probab. 35 (4) 1333 - 1350, July 2007.


Published: July 2007
First available in Project Euclid: 8 June 2007

zbMATH: 1129.60060
MathSciNet: MR2330974
Digital Object Identifier: 10.1214/009117906000001204

Primary: 60H15
Secondary: 76S05

Keywords: Harnack inequality , stochastic generalized porous medium equation , ultracontractivity

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 4 • July 2007
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