Boundary value problems for general first-order elliptic differential operators

Abstract

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.

Link to video abstract and material on the Fredholm property added

References in corpus (1)

• The kernel of the Rarita-Schwinger operator on Riemannian spin manifolds

Cited by in corpus (5)

• Functional calculus and harmonic analysis in geometry
• Boundary Value Problems for Dirac Operators on Graphs
• Elliptic Pre-Complexes, Hodge-like Decompositions and Overdetermined Boundary-Value Problems
• Local index theory for geometric first-order differential operators
• First-order elliptic boundary value problems on manifolds with non-compact boundary