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<\infty. Under suitable ellipticity assumptions we can define a family of complex powers A^z. 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.

Bounded imaginary powers of differential operators on manifolds with conical singularities

CORIASCO, Sandro;SEILER, JOERG
2003-01-01

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
2003
244
235
269
http://arxiv.org/pdf/math/0106008v2
Complex powers; Manifolds with conical singularities
S. CORIASCO; SCHROHE E.; SEILER J.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/3959
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