References
J. M. Ball & V. J. Mizel, Singular minimisers for regular one-dimensional problems in the calculus of variations. Bull. Amer. Math. Soc. 11 (1984), 143–146.
J. M. Ball & V. J. Mizel, One-dimensional variational problems whose minimisers do not satisfy the Euler-Lagrange equation. Arch. Rational Mech. Anal. 90 (1985), 325–388.
L. Cesari, Optimisation—Theory and Applications. Springer-Verlag, New York 1983.
F. Clarke & E. Vinter, Regularity properties of solutions to the basic problem in the calculus of variations. Trans. Amer. Math. Soc. 289 (1984), 73–98.
F. Clarke & R. Vinter, Regularity of solutions to variational problems with polynomial Lagrangians, to appear.
M. Lavrentiev, Sur quelques problèmes du calcul des variations. Ann. Mat. Pura Appl. 4 (1926), 7–28.
B. Mania, Sopra un esempio di Lavrentieff, Bull. Un. Mat. Ital. 13 (1934), 147–153.
L. Tonelli, Fondamenti di Calcolo delle Variazioni, Zanichelli 1923, Vol. II, p. 359.
Author information
Authors and Affiliations
Additional information
Communicated by J. M. Ball
Rights and permissions
About this article
Cite this article
Davie, A.M. Singular minimisers in the calculus of variations in one dimension. Arch. Rational Mech. Anal. 101, 161–177 (1988). https://doi.org/10.1007/BF00251459
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00251459