Bounded H∞-calculus for a degenerate elliptic boundary value problem

Abstract

We consider a strongly elliptic second order differential operator A together with a degenerate boundary operator T of the form T = φ0γ0 + φ1γ1, where γ0 and γ1 denote the evaluation of a function and its exterior normal derivative, respectively, at the boundary. We assume that φ0, φ1 ≥ 0 and φ0 + φ1 ≥ c > 0. We show that a suitable shift of the realization AT of A in Lp(X+) has a bounded H∞-calculus whenever X+ is a manifold with boundary and bounded geometry.