Gradient estimates for perturbed Ornstein-Uhlenbeck semigroups on infinite-dimensional convex domains

摘要

Let X be a separable Hilbert space endowed with a non-degenerate centred Gaussian measure gamma, and let lambda(1) be the maximum eigenvalue of the covariance operator associated with gamma. The associated Cameron-Martin space is denoted by H. For a sufficiently regular convex function U : X -> R and a convex set Omega subset of X, we set nu := e(-U) gamma and we consider the semigroup (T-Omega(t))(t >= 0) generated by the self-adjoint operator defined via the quadratic form