arXiv:1307.3021 Abstract | arXiv Analytics

arXiv:1307.3021 [math.DG]Abstract References Reviews Resources

Guide to Boundary Value Problems for Dirac-Type Operators

Published 2013-07-11, updated 2024-10-01Version 2

We present an introduction to boundary value problems for Dirac-type operators on complete Riemannian manifolds with compact boundary. We introduce a very general class of boundary conditions which contains local elliptic boundary conditions in the sense of Lopatinskij and Shapiro as well as the Atiyah-Patodi-Singer boundary conditions. We discuss boundary regularity of solutions and also spectral and index theory. The emphasis is on providing the reader with a working knowledge.

Comments: 30 pages, 2 figures, identical with published version up to layout

Journal: W. Ballmann et al. (eds.), Arbeitstagung Bonn 2013, Progress in Mathematics 319 (Springer, Basel, 2016), pp. 43-80

DOI: 10.1007/978-3-319-43648-7_3

Categories: math.DG, math.AP, math.SP

Subjects: 35J56, 58J05, 58J20, 58J32

Keywords: boundary value problems, dirac-type operators, contains local elliptic boundary conditions, complete riemannian manifolds, atiyah-patodi-singer boundary conditions

Tags: journal article

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