We prove the existence of a bounded H_infty-calculus in weighted L^p-Sobolev spaces for a closed extension A_T of a differential operator A on a conic manifold with boundary, subject to a differential boundary condition T, provided the resolvent exists in a sector of the complex plane and has a certain pseudodifferential structure that we describe. In case A_T is the minimal extension of A, this condition reduces to parameter-ellipticity of the boundary value problem (A,T). Examples concern the Dirichlet and Neumann Laplacians.

Bounded H_infty-Calculus for Differential Operators on Conic Manifolds with Boundary

CORIASCO, Sandro;SEILER, JOERG
2007-01-01

Abstract

We prove the existence of a bounded H_infty-calculus in weighted L^p-Sobolev spaces for a closed extension A_T of a differential operator A on a conic manifold with boundary, subject to a differential boundary condition T, provided the resolvent exists in a sector of the complex plane and has a certain pseudodifferential structure that we describe. In case A_T is the minimal extension of A, this condition reduces to parameter-ellipticity of the boundary value problem (A,T). Examples concern the Dirichlet and Neumann Laplacians.
2007
32,2
229
255
http://arxiv.org/pdf/math/0507081v1
Boundary value problems; H_infty-calculus; Manifolds with conical singularities.
S. CORIASCO; E. SCHROHE; J. SEILER
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/3969
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 16
social impact