On the existence of variations, possibly with pointwise gradient constraints
Simone Bertone; Arrigo Cellina
ESAIM: Control, Optimisation and Calculus of Variations (2007)
- Volume: 13, Issue: 2, page 331-342
- ISSN: 1292-8119
Access Full Article
topAbstract
topHow to cite
topReferences
top- V.I. Arnold, Mathematical methods of classical mechanics, Graduate Texts in Mathematics60, Springer-Verlag, New York, Heidelber, Berlin.
- H. Brezis, Analyse fonctionnelle, théorie et applications. Masson, Paris (1983).
- A. Cellina, On minima of a functional of the gradient: necessary conditions. Nonlinear Anal. 20 (1993) 337–341.
- A. Cellina, On minima of a functional of the gradient: sufficient conditions. Nonlinear Anal. 20 (1993) 343–347.
- A. Cellina and S. Perrotta, On the validity of the maximum principle and of the Euler-Lagrange equation for a minimum problem depending on the gradient. SIAM J. Control Optim.36 (1998) 1987–1998.
- L.C. Evans, Partial Differential Equations, Graduate Studies in Mathematics19, American Mathematical Society, Providence, Rhode Island (1998).
- L.C. Evans and W. Gangbo, Differential equations methods for the Monge-Kantorovich mass transfer problem, Mem. Amer. Math. Soc.137 (1999) 653.
- L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL (1992).
- M. Tsuji, On Lindelöf's theorem in the theory of differential equations. Jap. J. Math.16 (1939) 149–161.