Closed extensions of a pair of linear operators and dynamic boundary value problems

摘要

The classical Friedrichs extension was generalized by Sauer Quaestiones Mathematicae, Vol. 16(1989), 239-249 to obtain the simultaneous extension of the operator pairwith X a complex Banach space and y a complex Hilbert space. The extension procedure includes the introduction of a third operator C0for which the formyields a norm in the subspace D0Certain symmetry conditions are also assumed. It was shown that for C0= B0, the extension could be used to obtain existence and uniqueness results for initial value problems for second order parabolic equations with dynamic boundary values.