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Über eine Verheftung elliptischer Randwert‐Probleme
Author(s) -
Schulze BertWolfgang
Publication year - 1979
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19790930117
Subject(s) - mathematics , operator (biology) , differential operator , pure mathematics , elliptic operator , boundary (topology) , mathematical analysis , biochemistry , chemistry , repressor , transcription factor , gene
The paper presents a proof of the following‐theorem. Let M be a compact closed C ∞ ‐manifold which is the union of two submanifolds X + , X − with common boundary Y. Furthermore, let A:C ∞ (M, E) → C ∞ (M, F) be an elliptic pseudo‐differential operator ( E, F complex vector bundles on M ) with the transmission property with respect to Y. Then we can conclude: If + and − are elliptic boundary value problems for the restrictions of A to X + and X − respectively then we find an elliptic pseudodifferential operator S on Y with\documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm ind}A^{\rm +} + {\rm ind}A^ - = {\rm ind }A + {\rm ind}S. $$\end{document}