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
DOI:
https://doi.org/10.1090/S1079-6762-99-00060-8
Published electronically:
April 6, 1999
MathSciNet review:
1679452
Full-text PDF Free Access
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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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- L. Nicolaescu, The Maslov index, the spectral flow, and decompositions of manifolds, Duke Math. J. 80 (1995), 485-533.
- M. E. Taylor, Pseudodifferential Operators and Nonlinear PDE, Birkhäuser, Boston, 1991.
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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
Email:
marius@math.missouri.edu
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