Bounded imaginary powers of differential operators on manifolds with conical singularities
Sandro Coriasco, E. Schrohe, J. Seiler · 2001
Abstract We study the minimal and maximal closed extension of a dif-ferential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted Lp-spaces over B, 1 < p <∞. Under suitable ellipticity assumptions we can define a family of complex powers Az, z ∈ C. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the so-lution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations. Mathematics Subject Classification (2000): 35J70, 47A10, 35K57 1