Sharp Interface Limit of Stochastic Cahn-Hilliard Equation with Singular Noise

We study the sharp interface limit of the two dimensional stochastic Cahn-Hilliard equation driven by two types of singular noise: a space-time white noise and a space-time singular divergence-type noise. We show that with appropriate scaling of the noise the solutions of the stochastic problems converge to the solutions of the determinisitic Mullins-Sekerka/Hele-Shaw problem.

Coercive Inequalities and U-Bounds on Step-Two Carnot Groups

We prove Poincaré and Logβ-Sobolev inequalities for a class of probability measures on step-two Carnot groups.