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Regularity and index theory for Dirac-Schr\"{o}dinger systems with Lipschitz coefficients

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Werner Ballmann (Universitat Bonn), Jochen Brüning (Humboldt Universitat), Gilles Carron (LMJL)

Analysis of PDEs · Submitted 7 Mar 2007

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this article we develop the Fredholm theory of Dirac-Schr\"{o}dinger systems with Lipschitz coefficients.

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arXiv IDmath/0703185 (version 1)
Pith IDXNQFVORE, Pith's permanent record of this paper and its review
CitationGilles Carron (LMJL), Jochen Br\"uning (Humboldt Universitat), Werner Ballmann (Universitat Bonn). "Regularity and index theory for Dirac-Schr\"{o}dinger systems with Lipschitz coefficients." arXiv:math/0703185 (2007). https://pith.science/paper/XNQFVORE
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,334 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.04 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; .

Dirac-Schr\"{o}dinger systems play a central role when modeling Dirac bundles and Dirac-Schr\"{o}dinger operators near the boundary, along ends or near other singularities of Riemannian manifolds. In this article we develop the Fredholm theory of Dirac-Schr\"{o}dinger systems with Lipschitz coefficients.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Dirac-Schr\"{o}dinger systems play a central role when modeling Dirac bundles and Dirac-Schr\"{o}dinger operators near the boundary, along ends or near other singularities of Riemannian manifolds. background 1.00 0.04 0.03 asserted 1.00
s1 In this article we develop the Fredholm theory of Dirac-Schr\"{o}dinger systems with Lipschitz coefficients. contribution 1.00 0.96 0.41 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

Dirac-Schr\"{o}dinger systems play a central role when modeling Dirac bundles and Dirac-Schr\"{o}dinger operators near the boundary, along ends or near other singularities of Riemannian manifolds. In this article we develop the Fredholm theory of Dirac-Schr\"{o}dinger systems with Lipschitz coefficients.

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