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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Boundary value problems for Dirac-type equations

Robert A. Bartnik1 / Piotr T. Chruściel2

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Citation Information: Journal für die reine und angewandte Mathematik. Volume 2005, Issue 579, Pages 13–73, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crll.2005.2005.579.13, July 2005

Publication History

Received:
22. Juli 2003
Published Online:
2005-07-27

Abstract

We prove regularity for a class of boundary value problems for first order elliptic systems, with boundary conditions determined by spectral decompositions, under coefficient differentiability conditions weaker than previously known. We establish Fredholm properties for Dirac-type equations with these boundary conditions. Our results include sharp solvability criteria, over both compact and non-compact manifolds; weighted Poincaré and Schrödinger-Lichnerowicz inequalities provide asymptotic control in the noncompact case.

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