Boundary value problems for elliptic differential operators of first order

Bär, Christian; Ballmann, Werner

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Boundary value problems for elliptic differential operators of first order

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.

Metadaten
Verfasserangaben:	Christian Bär ORCiD GND, Werner Ballmann
URN:	urn:nbn:de:kobv:517-opus-60023
Schriftenreihe (Bandnummer):	Preprints des Instituts für Mathematik der Universität Potsdam (1(2012)18)
Publikationstyp:	Preprint
Sprache:	Englisch
Erscheinungsjahr:	2012
Veröffentlichende Institution:	Universität Potsdam
Datum der Freischaltung:	06.07.2012
Freies Schlagwort / Tag:	Elliptic operators; boundary regularity; coercivity; completeness; elliptic boundary conditions
Quelle:	arXiv:1101.1196v2 [math.DG] 21 Nov 2011
Organisationseinheiten:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC-Klassifikation:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Klassifikation:	35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J56 Boundary value problems for first-order elliptic systems
	58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx] / 58J05 Elliptic equations on manifolds, general theory [See also 35-XX]
	58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx] / 58J20 Index theory and related fixed point theorems [See also 19K56, 46L80]
	58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx] / 58J32 Boundary value problems on manifolds
Sammlung(en):	Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2012
Lizenz (Deutsch):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz
Externe Anmerkung:	RVK-Klassifikation: SI 990

Boundary value problems for elliptic differential operators of first order

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