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Guide to Elliptic Boundary Value Problems for Dirac-Type Operators

  • Christian Bär
  • Werner Ballmann
Chapter
Part of the Progress in Mathematics book series (PM, volume 319)

Abstract

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 contain local elliptic boundary conditions in the sense of Lopatinski 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.

Keywords

Operators of Dirac type Boundary conditions Boundary regularity Coercivity Coercivity at infinity Spectral theory Index theory Decomposition theorem Relative index theorem Cobordism theorem 

2010 Mathematics Subject Classification.

35J56 58J05 58J20 58J32. 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institut für Mathematik, Universität PotsdamPotsdamGermany
  2. 2.Max Planck Institute for MathematicsBonnGermany

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