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

DOI:
https://doi.org/10.1090/S0002-9947-97-01860-6

MathSciNet review:
1401786

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-97-01860-6

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