On the optimal regularity of plate equations with randomized time‐dependent coefficients

Abstract

AbstractFor plate equations with randomized coefficients, the joint influence from the principal operator, stochastic processes and oscillating coefficients, is of prime concern in the discussion of regularity of the solutions. We will apply the sophisticated techniques from stochastic partial differential equations and microlocal analysis to explore the upper bound of loss of regularity. Furthermore, in order to demonstrate the optimality of the estimates, appropriate counter‐examples with periodic coefficients will be constructed to show the lower bound of loss of regularity by the application of harmonic analysis and instability arguments.