Harnack inequality and applications for stochastic generalized porous media equations

• 成果类型: Article
• 署名作者: Wang, Feng-Yu
• 署名单位: Beijing Normal University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000001204
• 发表日期: 2007
• 页码: 1333-1350
• 关键词: logarithmic sobolev inequalities; functional inequalities; diffusion-processes; time asymptotics; semigroups

摘要

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.