The strong Feller property for singular stochastic PDEs
We show that the Markov semigroups generated by a large class of singular
stochastic PDEs satisfy the strong Feller property. These include for example
the KPZ equation and the dynamical $\Phi^4_3$ model. As a corollary, we prove
that the Brownian bridge measure is the unique invariant measure for the KPZ
equation with periodic boundary conditions.