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On Bojarski's index formula for nonsmooth interfaces


Author: Marius Mitrea
Journal: Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 40-46
MSC (1991): Primary 58G10, 42B20; Secondary 34L40, 30D55
Published electronically: April 6, 1999
MathSciNet review: 1679452
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Abstract: Let $D$ be a Dirac type operator on a compact manifold ${\mathcal{M}}$ and let $\Sigma $ be a Lipschitz submanifold of codimension one partitioning ${\mathcal{M}}$ into two Lipschitz domains $\Omega _{\pm }$. Also, let ${\mathcal{H}}^{p}_{\pm }(\Sigma ,D)$ be the traces on $\Sigma $ of the ($L^{p}$-style) Hardy spaces associated with $D$ in $\Omega _{\pm }$. Then $({\mathcal{H}}^{p}_{-}(\Sigma ,D),{\mathcal{H}}^{p}_{+}(\Sigma ,D))$ is a Fredholm pair of subspaces for $L^{p}(\Sigma )$ (in Kato's sense) whose index is the same as the index of the Dirac operator $D$ considered on the whole manifold ${\mathcal{M}}$.


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Additional Information

Marius Mitrea
Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211
Email: marius@math.missouri.edu

DOI: http://dx.doi.org/10.1090/S1079-6762-99-00060-8
PII: S 1079-6762(99)00060-8
Received by editor(s): December 2, 1998
Published electronically: April 6, 1999
Additional Notes: Partially supported by NSF
Communicated by: Stuart Antman
Article copyright: © Copyright 1999 American Mathematical Society