A hitchhiker's guide to first-order elliptic boundary value problems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918163898171392 |
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| author | Baer, Christian Bandara, Lashi |
| author_facet | Baer, Christian Bandara, Lashi |
| contents | To empower the mathematical hitchhiker wishing to use operator methods in geometry and topology, we present this user's guide to first-order elliptic boundary value problems. Existence, regularity, and Fredholmness are discussed for general first-order elliptic operators on manifolds with compact boundary. The focus is on a very general class of elliptic boundary conditions, which contain those that are pseudo-local as a special case, yielding the relative index theorem. A new characterisation of a subclass of elliptic boundary conditions is also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A hitchhiker's guide to first-order elliptic boundary value problems Baer, Christian Bandara, Lashi Analysis of PDEs Differential Geometry 35J56, 58J32 To empower the mathematical hitchhiker wishing to use operator methods in geometry and topology, we present this user's guide to first-order elliptic boundary value problems. Existence, regularity, and Fredholmness are discussed for general first-order elliptic operators on manifolds with compact boundary. The focus is on a very general class of elliptic boundary conditions, which contain those that are pseudo-local as a special case, yielding the relative index theorem. A new characterisation of a subclass of elliptic boundary conditions is also given. |
| title | A hitchhiker's guide to first-order elliptic boundary value problems |
| topic | Analysis of PDEs Differential Geometry 35J56, 58J32 |
| url | https://arxiv.org/abs/2510.16919 |