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

Abstract

The classical Friedrichs extension was generalized by Sauer [Quaestiones Mathematicae, Vol. 16(1989), 239-249] to obtain the simultaneous extension of the operator pair with X a complex Banach space and y a complex Hilbert space. The extension procedure includes the introduction of a third operator C₀ for which the form yields 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.

In the paper it is shown that the restriction of symmetry may be removed and that wider choices of C₀ lead to existence and uniqueness results for a larger class of dynamic boundary value problems.

Keywords:

• stonrgly elliptic
• Friedrichs' extension
• hermtian