Large deviation principles and Malliavin derivative for mean reflected stochastic differential equations

In this paper, we consider a class of reflected stochastic differential equations for which the constraint is not on the paths of the solution but on its law. We establish a small noise large deviation principle, a large deviation for short time and the Malliavin derivative. To prove large deviation principles, a sufficient condition for the weak convergence method, which is suitable for Mckean-Vlasov stochastic differential equation, plays an important role.