Differential operators with generalized constant coefficients.
Dirichlet problem for parabolic equations on Hilbert spaces
We study a linear second order parabolic equation in an open subset of a separable Hilbert space, with the Dirichlet boundary condition. We prove that a probabilistic formula, analogous to one obtained in the finite-dimensional case, gives a solution to this equation. We also give a uniqueness result.
Dissipative sets and nonlinear perturbated equations in Banach spaces