Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T07:41:06.277Z Has data issue: false hasContentIssue false
  • English
  • Français

On The Lavrentiev Phenomenon

Published online by Cambridge University Press:  20 November 2018

Philip D. Loewen
Philip D. Loewen*
Affiliation:
Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec, Canada H3C 3J7
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.

A new look at Manià's classical example of the Lavrentiev Phenomenon leads to several pertinent observations.

Keywords

49A05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 1 , 01 March 1987 , pp. 102 - 108
Copyright
Copyright © Canadian Mathematical Society 01

References

1. Angell, T. S.. A note on approximation of optimal solutions of free problems of the calculus of variations. Rend. Circ. Math. Palermo (2) 28 (1979), 258–272.Google Scholar
2. Ball, J. and Mizel, V.. Singular minimizers for regular one-dimensional problems in the calculus of variations. Bull. AMS 11 (1984), 143–146.Google Scholar
3. Ball, J. and Mizel, V.. One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation. Arch. Rat. Mech. Anal. 90 (1985), 325–388.Google Scholar
4. Cesari, L.. Optimization — Theory and Applications: Problems with Ordinary differential equations. New York: Springer-Verlag, 1983.Google Scholar
5. Cesari, L. and Angell, T. S.. On the Lavrentiev phenomenon. Preprint, 1985.Google Scholar
6. Clarke, Frank H.. Optimization and Nonsmooth Analysis. New York: Wiley-Interscience, 1983.Google Scholar
7. Clarke, Frank H. and Vinter, Richard B.. Regularity properties of solutions to the basic problem in the calculus of variations. Trans. AMS 289 (1985), 73–98.Google Scholar
8. Clarke, Frank H. and Vinter, Richard B.. Existence and Regularity in the small in the calculus of variations. J. Diff. Eqns. 59 (1985), 336-354.Google Scholar
9. Clarke, Frank H. and Vinter, Richard B.. Regularity of solutions to variational problems with polynomial Lagrangians. Bull. Pol. Acad. Sci., 34 (1986), 73-81.Google Scholar
10. Lavrentiev, M.. Sur quelques problèmes du calcul des variations. Annali di Matematica, Pura et Applicata 4(1926), 7–28.Google Scholar
11. Manià, B.. Sopra un esempio di Lavrentieff. Boll. Un. Mat. Ital. 13 (1934), 147–153.Google Scholar