Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Multi-dimensional Morse Index Theorems and a symplectic view of elliptic boundary value problems
HTML articles powered by AMS MathViewer

by Jian Deng and Christopher Jones PDF
Trans. Amer. Math. Soc. 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
Similar Articles
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