Study on stochastic partial differential equations with singular coefficients

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We have studied the nonequilibrium fluctuation limit for the motion of two dimensional Young diagrams from the aspect of interface model. The limit is described by a certain stochastic partial differential equation. Moreover, the equilibrium solution of the equation which describes the growth of interfaces in consideration of the random fluctuation effect in space and time, the stochastic entropic solution of the stochastic partial differential equation with fractional differential operators, blow-up problem in a harmonic map heat flow, the singular limit of anisotropic Allen-Cahn equations and precise estimates on the position of the interfaces are studied.