School of Mathematics, The University of New South Wales, Sydney 2052, Australia, e-mail: B.Goldys@unsw.edu.au
Abstract: We show that solutions to some Hamilton-Jacobi Equations associated to the problem of optimal control of stochastic semilinear equations enjoy the hypercontractivity property.
Keywords: Hamilton-Jacobi equation, stochastic semilinear equation, invariant measure, Log-Sobolev inequality, hypercontractivity
Classification (MSC 2000): 60H15
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