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Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions

Journal article
Authors L. Bandara
Andreas Rosén
Published in Communications in Partial Differential Equations
ISSN 0360-5302
Publication year 2019
Published at Department of Mathematical Sciences
Language en
Links dx.doi.org/10.1080/03605302.2019.16...
Keywords Boundary value problems, Dirac operator, functional calculus, real-variable harmonic analysis, Riesz, spectral flow, Mathematics
Subject categories Mathematics

Abstract

On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah-Singer Dirac operator in depends Riesz continuously on perturbations of local boundary conditions The Lipschitz bound for the map depends on Lipschitz smoothness and ellipticity of and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius away from a compact neighbourhood of the boundary. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.

Page Manager: Webmaster|Last update: 9/11/2012
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