Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-25T00:37:48.052Z Has data issue: false hasContentIssue false
  • English
  • Français

Second order elliptic boundary value problems in spaces with homogeneous norms

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  09 April 2009

A. J. Pryde
A. J. Pryde
Affiliation:
School of Mathematics and Physics Macquarie UniversityNorth Ryde, N.S.W. 2113, Australia
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 the interior and Dirichiet problems and problems with first order boundary conditions, for a second order homogeneous elliptic partial differential operator with constant coefficients. Under natural conditions on the operators, these problems give rise to isomorphisms between the appropriate spaces with homogeneous norms. From there we obtain a priori estimates and regularity results for boundary value problems in Sobolev spaces.

MSC classification

Secondary: 35J25: Boundary value problems for second-order elliptic equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 1 , February 1980 , pp. 1 - 13
Copyright
Copyright © Australian Mathematical Society 1980

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.Google Scholar
Browder, F. E. (1959), ‘Estimates and existence theorems for elliptic boundary value problems’, Proc. Nat. Acad. Sci. U.S.A. 45, 365–372.Google Scholar
Pryde, A. J. (1977), ‘The five lemma for Banach spaces’, Proc. Amer. Math. Soc. 65 (1), 37–43.Google Scholar
Pryde, A. J. (1979a), ‘Spaces with homogeneous norms’, Bull. Austral. Math. Soc. (to appear).Google Scholar
Pryde, A. J. (1979b), ‘Second order elliptic equations with mixed boundary conditions’, submitted.Google Scholar
Schechter, M. (1959), ‘Integral inequalities for partial differential operators and functions satisfying general boundary conditions’, Comm. Pure Appl. Math. 12, 37–66.Google Scholar