An index formula for elliptic systems

in the plane

Author:
B. Rowley

Journal:
Trans. Amer. Math. Soc. **349** (1997), 3149-3179

MSC (1991):
Primary 35J40, 35J55, 15A22

MathSciNet review:
1401785

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Abstract | References | Similar Articles | Additional Information

Abstract: An index formula is proved for elliptic systems of P.D.E.'s with boundary values in a simply connected region in the plane. Let denote the elliptic operator and the boundary operator. In an earlier paper by the author, the algebraic condition for the Fredholm property, i.e. the Lopatinskii condition, was reformulated as follows. On the boundary, a square matrix function defined on the unit cotangent bundle of was constructed from the principal symbols of the coefficients of the boundary operator and a spectral pair for the family of matrix polynomials associated with the principal symbol of the elliptic operator. The Lopatinskii condition is equivalent to the condition that the function have invertible values. In the present paper, the index of is expressed in terms of the winding number of the determinant of .

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Additional Information

**B. Rowley**

Affiliation:
Department of Mathematics, Champlain College, Lennoxville, Quebec, Canada

Email:
browley@abacom.com

DOI:
http://dx.doi.org/10.1090/S0002-9947-97-01859-X

Keywords:
Elliptic boundary value problems,
matrix polynomials,
index formula,
Riemann-Hilbert problem

Received by editor(s):
August 16, 1994

Article copyright:
© Copyright 1997
American Mathematical Society