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.File in questo prodotto:
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