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Elliptic equations in open subsets of infinite dimensional Hilbert spaces

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Stochastic Partial Differential Equations

We consider the equation

$$ lambda phi -Lphi = f $$

where $lambda geq 0$; and L is the Ornstein{Uhlenbeck operator defined in an open subset O of a Hilbert space H, equipped with Dirichlet or Neumann boundary conditions on the boundary of O. We discuss some existence and regularity results of the solution u of the above equation when the given function f belongs to the $L^2(O; mu)$ and $mu$ is the invariant measure of L

This talk is part of the Isaac Newton Institute Seminar Series series.

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