Bounded imaginary powers of differential operators on manifolds with conical singularities |
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| Authors: | S. Coriasco E. Schrohe J. Seiler |
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| Affiliation: | 1.Universitá di Torino, Dipartimento di Matematica, Via Carlo Alberto 10, 10123 Torino, Italy (e-mail: coriasco@dm.unito.it),IT;2.Universit?t Potsdam, Institut für Mathematik, Postfach 60 15 53, 14415 Potsdam, Germany (e-mail: schrohe@math.uni-potsdam.de),DE;3.Universit?t Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, Germany (e-mail: seiler@ifam.uni-hannover.de),DE |
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| Abstract: | We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted L p -spaces over B, 1<p<∞. Under suitable ellipticity assumptions we can define a family of complex powers A z , zℂ. 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 solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations. Received: 12 June 2001; in final form: 3 June 2002 / Published online: 1 April 2003 Mathematics Subject Classification (2000): 35J70, 47A10, 35K57 |
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