A hitchhiker's guide to first-order elliptic boundary value problems
Analysis of PDEs
2025-10-21 v1 Differential Geometry
Abstract
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.
Cite
@article{arxiv.2510.16919,
title = {A hitchhiker's guide to first-order elliptic boundary value problems},
author = {Christian Baer and Lashi Bandara},
journal= {arXiv preprint arXiv:2510.16919},
year = {2025}
}
Comments
17 pages