Riesz continuity of the Atiyah–Singer Dirac operator under perturbations of local boundary conditions
- 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.
Author details: | Menaka Lashitha BandaraORCiD, Andreas RosénORCiD |
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URN: | urn:nbn:de:kobv:517-opus4-434078 |
DOI: | https://doi.org/10.25932/publishup-43407 |
ISSN: | 1866-8372 |
Title of parent work (English): | Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe |
Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (758) |
Publication type: | Postprint |
Language: | English |
Date of first publication: | 2019/10/23 |
Publication year: | 2019 |
Publishing institution: | Universität Potsdam |
Release date: | 2019/10/23 |
Tag: | Dirac operator; Riesz continuity; boundary value problems; functional calculus; real-variable harmonic analysis; spectral flow |
Issue: | 758 |
Number of pages: | 33 |
First page: | 1253 |
Last Page: | 1284 |
Source: | Communications in Partial Differential Equations 44 (2019) 12, S. 1253–1284 DOI: 10.1080/03605302.2019.1611847 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access |
License (German): | CC-BY-NC-ND - Namensnennung, nicht kommerziell, keine Bearbeitungen 4.0 International |
External remark: | Bibliographieeintrag der Originalveröffentlichung/Quelle |