Elliptic equations in open subsets of infinite dimensional Hilbert spaces
Seminar Room 1, Newton Institute
We consider the equation
\lambda \phi -L\phi = 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.