TY - JOUR

T1 - The resolvent of closed extensions of cone differential operators

AU - Schrohe, E.

AU - Seiler, J.

N1 - Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2005/8

Y1 - 2005/8

N2 - We study closed extensions A of an elliptic differential operator A on a manifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent (λ - A)-1 exists in a sector of the complex plane and decays like 1/|λ| as |λ| → ∞. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of A. 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 u̇ - Δu = f, u(0) = 0.

AB - We study closed extensions A of an elliptic differential operator A on a manifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent (λ - A)-1 exists in a sector of the complex plane and decays like 1/|λ| as |λ| → ∞. Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of A. 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 u̇ - Δu = f, u(0) = 0.

KW - Manifolds with conical singularities

KW - Maximal regularity

KW - Resolvent

UR - http://www.scopus.com/inward/record.url?scp=24144496907&partnerID=8YFLogxK

U2 - 10.4153/CJM-2005-031-1

DO - 10.4153/CJM-2005-031-1

M3 - Article

AN - SCOPUS:24144496907

VL - 57

SP - 771

EP - 811

JO - Canadian journal of mathematics

JF - Canadian journal of mathematics

SN - 0008-414X

IS - 4

ER -