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Higher order elliptic boundary value problems in spaces with homogeneous norms

Part of: Elliptic equations and systems Equations and systems with constant coefficients

Published online by Cambridge University Press:  09 April 2009

A. J. Pryde
A. J. Pryde
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada
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Abstract

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We consider general boundary value problems for homogeneous elliptic partial differential operators with constant coefficients. Under natural conditions on the operators, these problems give rise to isomorphisms between the appropriate spaces with homogeneous norms. We also consider operators which are not properly elliptic and boundary systems which do not satisfy the complementing condition and determine when they give rise to left or right invertible operators. A priori inequalities and regularity results for the corresponding boundary value problems in Sobolev spaces are then readily obtained.

MSC classification

Secondary: 35J40: Boundary value problems for higher-order elliptic equations 35E20: General theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 1 , June 1981 , pp. 92 - 113
Copyright
Copyright © Australian Mathematical Society 1981

References

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