Strong Feller Property and Irreducibility for Non-Linear Monotone SPDEs

TL;DR

This paper investigates the strong Feller property and irreducibility of certain non-linear monotone SPDEs with multiplicative noise, analyzing the regularity of their Markov semigroups and applying results to specific equations like porous media and fast diffusion.

Contribution

It establishes conditions for strong Feller and irreducibility in non-linear monotone SPDEs and discusses Hölder continuity of the associated semigroups in special cases.

Findings

Proves strong Feller property for classes of non-linear monotone SPDEs.

Shows irreducibility under certain conditions.

Applies results to stochastic porous media and fast diffusion equations.

Abstract

Strong Feller property and irreducibility are study for a class of non-linear monotone stochastic partial differential equations with multiplicative noise. H\"older 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.