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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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
Trans. Amer. Math. Soc. 363 (2011), 1487-1508 Request permission


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.
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Additional Information
  • Jian Deng
  • Affiliation: CEMA, Central University of Finance and Economics, Beijing, People’s Republic of China, 100085
  • Email:
  • 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:
  • 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:
  • MathSciNet review: 2737274