Boundary value problems for general first-order elliptic differential operators
- We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local.We show the equivalence of various characterisations of elliptic boundary conditions and demonstrate how the boundary conditions traditionally considered in the literature fit in our framework. The regularity of the solutions up to the boundary is proven. We show that imposing elliptic boundary conditions yields a Fredholm operator if the manifold is compact. We provide examples which are conveniently treated by our methods.
| Author details: | Christian BärORCiDGND, Lashi BandaraORCiD |
|---|---|
| DOI: | https://doi.org/10.1016/j.jfa.2022.109445 |
| ISSN: | 0022-1236 |
| ISSN: | 1096-0783 |
| Title of parent work (English): | Journal of functional analysis |
| Publisher: | Elsevier |
| Place of publishing: | Amsterdam [u.a.] |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2022/06/15 |
| Publication year: | 2022 |
| Release date: | 2023/12/07 |
| Tag: | Fredholm property; H-infinity-functional calculus; Rarita-Schwinger; boundary regularity; conditions; elliptic boundary; elliptic differential operators of firstorder; maximal regularity; operator |
| Volume: | 282 |
| Issue: | 12 |
| Article number: | 109445 |
| Number of pages: | 69 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
