On regularity of invariant measures of multivalued stochastic differential equations

We prove that the invariant measure associated to a multivalued stochastic differential equation is absolutely continuous with respect to the Lebesgue measure with a density ρ ∈ B loc s , p , q for all 1 < p < d / ( d − 1 ) , 0 < s < 1 and q ⩾ 1 , and ρ ∈ W 1 , q ( O ) for all q > 1 provided that O ⋐ Int ( D ( A ) ) . In particular, ρ is locally α -Hölder continuous in Int ( D ( A ) ) for all α < 1 .