First-order elliptic boundary value problems on manifolds with non-compact boundary
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917264951869440 |
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| author | Baer, Christian Bandara, Lashi |
| author_facet | Baer, Christian Bandara, Lashi |
| contents | We consider first-order elliptic differential operators acting on vector bundles over smooth manifolds with smooth boundary, which is permitted to be noncompact. Under very mild assumptions, we obtain a regularity theory for sections in the maximal domain. Under additional geometric assumptions, and assumptions on an adapted boundary operator, we obtain a trace theorem on the maximal domain. This allows us to systematically study both local and nonlocal boundary conditions. In particular, the Atiyah-Patodi-Singer boundary condition occurs as a special case. Furthermore, we study contexts which induce semi-Fredholm and Fredholm extensions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_17784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | First-order elliptic boundary value problems on manifolds with non-compact boundary Baer, Christian Bandara, Lashi Differential Geometry Analysis of PDEs Primary 35J56, 47A53, 58J05, 58J32, Secondary 46E35, 53C21 We consider first-order elliptic differential operators acting on vector bundles over smooth manifolds with smooth boundary, which is permitted to be noncompact. Under very mild assumptions, we obtain a regularity theory for sections in the maximal domain. Under additional geometric assumptions, and assumptions on an adapted boundary operator, we obtain a trace theorem on the maximal domain. This allows us to systematically study both local and nonlocal boundary conditions. In particular, the Atiyah-Patodi-Singer boundary condition occurs as a special case. Furthermore, we study contexts which induce semi-Fredholm and Fredholm extensions. |
| title | First-order elliptic boundary value problems on manifolds with non-compact boundary |
| topic | Differential Geometry Analysis of PDEs Primary 35J56, 47A53, 58J05, 58J32, Secondary 46E35, 53C21 |
| url | https://arxiv.org/abs/2401.17784 |