First-order elliptic boundary value problems on manifolds with non-compact boundary

Abstract

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.

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References in corpus (4)

• Boundary Value Problems for Elliptic Differential Operators of First Order
• Boundary value problems for noncompact boundaries of Spin${}^c$ manifolds and spectral estimates
• Boundary value problems for general first-order elliptic differential operators
• Cauchy data spaces and Atiyah-Patodi-Singer index on non-compact manifolds