Strong Feller Property and Irreducibility for Non-Linear Monotone SPDEs

2014/07/27 by Zhang, Shao-Qin
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1407.7222

Abstract

Strong Feller property and irreducibility are study for a class of non-linear monotone stochastic partial differential equations with multiplicative noise. Hölder continuity of the associated Markov semigroups are discussed in some special cases. The main results are applied to several examples such as stochastic porous media equations, stochastic fast diffusion equations.

Related

• Strong solutions for SPDE with locally monotone coefficients driven by Lévy noise
• Asymptotic Log-Harnack Inequality for Monotone SPDE with Multiplicative Noise
• The strong Feller property for singular stochastic PDEs
• Harnack Inequality for Semilinear spdes with multiplicative noise
• Well-posedness of a class of stochastic partial differential equations with fully monotone coefficients perturbed by Lévy noise