Characterization of the Domain of Fractional Powers of a Class of Elliptic Differential Operators with Feedback Boundary Conditions

We study a class of elliptic differential operators with feedback boundary conditions of the Dirichlet type and the generalized Neumann type. The domain of the fractional powers of these operators is completely characterized in terms of various Sobolev spaces. The results are an extension of the standard results of Fujiwara [Proc. Japan. Acad. Ser. A43, 1967] and Grisvard [Arch. Rational Mech. Anal.25, 1967].