Second order unbounded parabolic equations in separated form
We prove existence and uniqueness of viscosity solutions of Cauchy problems for fully nonlinear unbounded second order Hamilton-Jacobi-Bellman-Isaacs equations deened on the product of two innnite dimensional Hilbert spaces H 0 H 00 , where H 00 is separable. The equations have a special \separated" form in a sense that the terms involving second derivatives are everywhere deened, continuous and depend only on derivatives with respect to x 00 2 H 00 , while the unbounded terms are of rst order and depend only on derivatives with respect to x 0 2 H 0 .