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Multi-dimensional Morse Index Theorems and a symplectic view of elliptic boundary value problems
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Deng, Jian and Jones, C. K. R. T. (Christopher K. R. T.) (2011) Multi-dimensional Morse Index Theorems and a symplectic view of elliptic boundary value problems. Transactions of the American Mathematical Society, Vol.363 (No.3). pp. 1487-1508. doi:10.1090/S0002-9947-2010-05129-3 ISSN 0002-9947.
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Official URL: http://dx.doi.org/10.1090/S0002-9947-2010-05129-3
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Boundary value problems, Sobolev spaces, Maslov index, Eigenvalues | ||||
Journal or Publication Title: | Transactions of the American Mathematical Society | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 0002-9947 | ||||
Official Date: | March 2011 | ||||
Dates: |
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Volume: | Vol.363 | ||||
Number: | No.3 | ||||
Page Range: | pp. 1487-1508 | ||||
DOI: | 10.1090/S0002-9947-2010-05129-3 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 18 December 2015 | ||||
Date of first compliant Open Access: | 18 December 2015 | ||||
Funder: | Guo jia zi ran ke xue ji jin wei yuan hui (China) [National Natural Science Foundation of China] (NSFC), National Science Foundation (U.S.) (NSF) | ||||
Grant number: | 10601014 (NSFC), DMS-0410267 (NSF) |
Data sourced from Thomson Reuters' Web of Knowledge
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