Problems for elliptic equations with operatorboundary conditions

We consider, in a Hilbert space H, a problem on [0,1] for a second order elliptic operator-differential equation with operator-boundary conditions. We also consider second order elliptic differential equations with operator-boundary conditions in cylindrical domains in the case when operator-boundary conditions contain integral terms over the whole domain. In this case, the proof of the density of the domain of definition of operators in a space is difficult. When boundary conditions are local, this fact is a simple corollary of the density ofC 0 (infinity)((omega)) inL p ((omega)).