Year: 2012
Type: article
Abstract: We study boundary value problems for linear elliptic differential operators of order one.The underlying manifold may be noncompact, but the boundary is assumed to be compact.We require a symmetry property of the principal symbol of the operator along the boundary.This is satisfied by Dirac type operators, for instance.We provide a selfcontained introduction to (nonlocal) elliptic boundary conditions, boundary regularity of solutions, and index theory.In particular, we simplify and generalize the traditional theory of elliptic boundary value problems for Dirac type operators.We also prove a related decomposition theorem, a general version of Gromov and Lawson's relative index theorem and a generalization of the cobordism theorem.
Source: Surveys in Differential Geometry
Authors: Werner Ballmann, Christian Bär
Institutions: Max Planck Institute for Mathematics, University of Potsdam
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2043641803