The Resolvent of Closed Extensions of Cone Differential Operators

Abstract

Abstract We study closed extensions of an elliptic differential operator A on amanifold with conical singularities, acting as an unbounded operator on a weighted L p -space. Under suitable conditions we show that the resolvent exists in a sector of the complex plane and decays like as Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of . As an application we treat the Laplace–Beltrami operator for a metric with straight conical degeneracy and describe domains yielding maximal regularity for the Cauchy problem , u (0) = 0.