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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Matrix polynomials and the
index problem for elliptic systems


Author: B. Rowley
Journal: Trans. Amer. Math. Soc. 349 (1997), 3105-3148
MSC (1991): Primary 35J45, 35J55, 15A22
MathSciNet review: 1401786
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Abstract: The main new results of this paper concern the formulation of algebraic conditions for the Fredholm property of elliptic systems of P.D.E.'s with boundary values, which are equivalent to the Lopatinskii condition. The Lopatinskii condition is reformulated in a new algebraic form (based on matrix polynomials) which is then used to study the existence of homotopies of elliptic boundary value problems. The paper also contains an exposition of the relevant parts of the theory of matrix polynomials and the theory of elliptic systems of P.D.E.'s.


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Additional Information

B. Rowley
Affiliation: Department of Mathematics, Champlain College, Lennoxville, Quebec, Canada
Email: browley@lennox.champlaincollege.qc.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01860-6
PII: S 0002-9947(97)01860-6
Keywords: Elliptic boundary value problems, matrix polynomials, Lopatinskii condition, Fredholm property
Received by editor(s): August 16, 1994
Received by editor(s) in revised form: February 12, 1996
Additional Notes: The author wishes to acknowledge that the abstract, the introduction and parts of §§2 and 3 were revised due to the helpful remarks and suggestions of the referee.
Article copyright: © Copyright 1997 American Mathematical Society