Analysis on regular corner spaces
- We establish a new approach of treating elliptic boundary value problems (BVPs) on manifolds with boundary and regular corners, up to singularity order 2. Ellipticity and parametrices are obtained in terms of symbols taking values in algebras of BVPs on manifolds of corresponding lower singularity orders. Those refer to Boutet de Monvel's calculus of operators with the transmission property, see Boutet de Monvel (Acta Math 126:11-51, 1971) for the case of smooth boundary. On corner configuration operators act in spaces with multiple weights. We mainly study the case of upper left entries in the respective 2 x 2 operator block-matrices of such a calculus. Green operators in the sense of Boutet de Monvel (Acta Math 126:11-51, 1971) analogously appear in singular cases, and they are complemented by contributions of Mellin type. We formulate a result on ellipticity and the Fredholm property in weighted corner spaces, with parametrices of analogous kind.
Author details: | Der-Chen ChangGND, Sara KhalilORCiDGND, Bert-Wolfgang SchulzeGND |
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DOI: | https://doi.org/10.1007/s12220-021-00614-3 |
ISSN: | 1050-6926 |
ISSN: | 1559-002X |
Title of parent work (English): | The journal of geometric analysis |
Publisher: | Springer |
Place of publishing: | New York |
Publication type: | Article |
Language: | English |
Date of first publication: | 2021/02/24 |
Publication year: | 2021 |
Release date: | 2024/05/23 |
Tag: | Boutet de Monvel's calculus; Kegel space; Mellin symbols with values in the edge calculus; Parametrices of elliptic operators; Pseudo-differential operators; Singular cones |
Volume: | 31 |
Issue: | 9 |
Number of pages: | 42 |
First page: | 9199 |
Last Page: | 9240 |
Funding institution: | NSF National Science Foundation (NSF) [DMS-1408839]; McDevitt Endowment Fund at Georgetown University |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |