Fractional powers and interpolation theory for multivalued linear operators and applications to degenerate differential equations

Abstract

We provide intermediate properties for the domains of the fractional powers of an abstract multivalued linear operator A of weak parabolic type. In particular, our results exhibit the special role played by the linear subspace A0, which reduces to {0} if and only if A is single-valued. The behaviour of the singular semigroup generated by A with respect to the domains of the fractional powers is then studied, and applications of this behaviour to questions of maximal time and space regularity for abstract multivalued evolution equations are given. As a concrete case we consider a class of degenerate partial differential evolution equations which may be rewritten in a multivalued evolution form.