Details
| Original language | English |
|---|---|
| Pages (from-to) | 229-255 |
| Number of pages | 27 |
| Journal | Communications in Partial Differential Equations |
| Volume | 32 |
| Issue number | 2 |
| Publication status | Published - 2 Mar 2007 |
Abstract
We prove the existence of a bounded H∞-calculus in weighted Lp-Sobolev spaces for a closed extension AT of a differential operator A on a conic manifold with boundary, subject to a differential boundary condition T, provided the resolvent (λ - A T)-1 exists in a sector Λ ⊂ ℂ and has a certain pseudodifferential structure that we describe. In case AT is the minimal extension of A, this condition reduces to parameter-ellipticity of the boundary value problem [TA]. Examples concern the Dirichlet and Neumann Laplacians.
Keywords
- Boundary value problems, H-calculus, Manifolds with conical singularities
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Communications in Partial Differential Equations, Vol. 32, No. 2, 02.03.2007, p. 229-255.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Bounded H∞-calculus for differential operators on conic manifolds with boundary
AU - Coriasco, S.
AU - Schrohe, E.
AU - Seiler, J.
N1 - Copyright: Copyright 2007 Elsevier B.V., All rights reserved.
PY - 2007/3/2
Y1 - 2007/3/2
N2 - We prove the existence of a bounded H∞-calculus in weighted Lp-Sobolev spaces for a closed extension AT of a differential operator A on a conic manifold with boundary, subject to a differential boundary condition T, provided the resolvent (λ - A T)-1 exists in a sector Λ ⊂ ℂ and has a certain pseudodifferential structure that we describe. In case AT is the minimal extension of A, this condition reduces to parameter-ellipticity of the boundary value problem [TA]. Examples concern the Dirichlet and Neumann Laplacians.
AB - We prove the existence of a bounded H∞-calculus in weighted Lp-Sobolev spaces for a closed extension AT of a differential operator A on a conic manifold with boundary, subject to a differential boundary condition T, provided the resolvent (λ - A T)-1 exists in a sector Λ ⊂ ℂ and has a certain pseudodifferential structure that we describe. In case AT is the minimal extension of A, this condition reduces to parameter-ellipticity of the boundary value problem [TA]. Examples concern the Dirichlet and Neumann Laplacians.
KW - Boundary value problems
KW - H-calculus
KW - Manifolds with conical singularities
UR - http://www.scopus.com/inward/record.url?scp=33847671799&partnerID=8YFLogxK
U2 - 10.1080/03605300600910290
DO - 10.1080/03605300600910290
M3 - Article
AN - SCOPUS:33847671799
VL - 32
SP - 229
EP - 255
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
SN - 0360-5302
IS - 2
ER -