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Electronic Research Announcements

ISSN 1079-6762



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
MR Author ID: 341602
ORCID: 0000-0002-5195-5953

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