Large Deviation Principle for McKean–Vlasov Quasilinear Stochastic Evolution Equations

This paper is devoted to investigating the Freidlin–Wentzell’s large deviation principle for a class of McKean–Vlasov quasilinear SPDEs perturbed by small multiplicative noise. We adopt variational framework and modified weak convergence criteria prove Laplace type SPDEs, which equivalent principle. Moreover, we do not assume any compactness condition embedding in Gelfand triple handle both cases bounded unbounded domains applications. The main results can be applied various such as distribution dependent stochastic porous media equations p-Laplace equations.