## Multi-dimensional Morse Index Theorems and a symplectic view of elliptic boundary value problems

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- by Jian Deng and Christopher Jones PDF
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**363**(2011), 1487-1508 Request permission

## Abstract:

Morse Index Theorems for elliptic boundary value problems in multi-dimensions are proved under various boundary conditions. The theorems work for star-shaped domains and are based on a new idea of measuring the “oscillation” of the trace of the set of solutions on a shrinking boundary. The oscillation is measured by formulating a Maslov index in an appropriate Sobolev space of functions on this boundary. A fundamental difference between the cases of Dirichlet and Neumann boundary conditions is exposed through a monotonicity that holds only in the former case.## References

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## Additional Information

**Jian Deng**- Affiliation: CEMA, Central University of Finance and Economics, Beijing, People’s Republic of China, 100085
- Email: jdeng@fudan.edu.cn
**Christopher Jones**- Affiliation: Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599 – and – Warwick Mathematics Institute, University of Warwick, United Kingdom
- MR Author ID: 95400
- ORCID: 0000-0002-2700-6096
- Email: ckrtj@email.unc.edu
- Received by editor(s): July 3, 2008
- Received by editor(s) in revised form: June 8, 2009
- Published electronically: October 15, 2010
- © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**363**(2011), 1487-1508 - MSC (2000): Primary 35J25, 35P15; Secondary 53D12, 35B05
- DOI: https://doi.org/10.1090/S0002-9947-2010-05129-3
- MathSciNet review: 2737274