Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T23:45:38.843Z Has data issue: false hasContentIssue false
  • English
  • Français

Higher order elliptic boundary value problems in spaces with homogeneous norms

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

Published online by Cambridge University Press:  09 April 2009

A. J. Pryde
A. J. Pryde
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Agmon, S., Douglis, A. and Nirenberg, L. (1959), ‘Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I’, Comm. Pure Appl. Math. 12, 623–727.CrossRefGoogle Scholar
Browder, F. E. (1959), ‘Estimates and existence theorems for elliptic boundary problems’, Proc. Nat. Acad. Sci. U.S.A. 45, 365–372.CrossRefGoogle Scholar
Pryde, A. J. (1977), ‘The five lemma for Banach spaces’, Proc. Amer. Math. Soc. 65, 37–43.CrossRefGoogle Scholar
Pryde, A. J. (1980a), ‘Spaces with homogeneous norms’, Bull. Austral. Math. Soc. 21, 189–205.CrossRefGoogle Scholar
Pryde, A. J. (1980b), ‘Second order elliptic boundary value problems in spaces with homogeneous norms’, J. Austral. Math. Soc. Ser. A 29, 1–13.Google Scholar
Pryde, A. J. (1981), ‘Second order elliptic equations with mixed boundary conditions’, J. Math. Anal. Appl., to appear.CrossRefGoogle Scholar
Schecter, M. (1959), ‘Integral inequalities for partial differential operators and functions satisfying general boundary conditions’, Comm. Pure Appl. Math. 12, 37–66.CrossRefGoogle Scholar
Van der Poorten, A. J. (1976), ‘Some determinants that should be better known’, J. Austral. Math. Soc. Ser. A 21, 278–288.CrossRefGoogle Scholar