Existence of Minimizers of Free Autonomous Variational Problems Via Solvability of Constrained Ones
Cupini, Giovanni ; Guidorzi, Marcello ; Marcelli, Cristina
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009), p. 1183-1205 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2009__26_4_1183_0,
     author = {Cupini, Giovanni and Guidorzi, Marcello and Marcelli, Cristina},
     title = {Existence of Minimizers of Free Autonomous Variational Problems Via Solvability of Constrained Ones},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {26},
     year = {2009},
     pages = {1183-1205},
     doi = {10.1016/j.anihpc.2008.06.006},
     mrnumber = {2542720},
     zbl = {1167.49002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_4_1183_0}
}

Cupini, Giovanni; Guidorzi, Marcello; Marcelli, Cristina. Existence of Minimizers of Free Autonomous Variational Problems Via Solvability of Constrained Ones. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 1183-1205. doi : 10.1016/j.anihpc.2008.06.006. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_4_1183_0/

[1] Botteron B., Dacorogna B., Existence of Solutions for a Variational Problem Associated to Models in Optimal Foraging Theory, J. Math. Anal. Appl. 147 (1990) 263-276. | MR 1044699 | Zbl 0717.49002

[2] Botteron B., Dacorogna B., Existence and Nonexistence Results for Noncoercive Variational Problems and Applications in Ecology, J. Differential Equations 85 (1990) 214-235. | MR 1054549 | Zbl 0714.49002

[3] Botteron B., Marcellini P., A General Approach to the Existence of Minimizers of One-Dimensional Noncoercive Integrals of the Calculus of Variations, Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991) 197-223. | Numdam | MR 1096604 | Zbl 0729.49002

[4] Celada P., Perrotta S., Existence of Minimizers for Nonconvex, Noncoercive Simple Integrals, SIAM J. Control Optim. 41 (2002) 1118-1140. | MR 1972505 | Zbl 1021.49011

[5] Cellina A., The Classical Problem of the Calculus of Variations in the Autonomous Case: Relaxation and Lipschitzianity of Solutions, Trans. Amer. Math. Soc. 356 (2004) 415-426. | MR 2020039 | Zbl 1064.49027

[6] Cellina A., Ferriero A., Existence of Lipschitzian Solutions to the Classical Problem of the Calculus of Variations in the Autonomous Case, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003) 911-919. | Numdam | MR 2008683 | Zbl 1030.49039

[7] Cellina A., Treu G., Zagatti S., On the Minimum Problem for a Class of Noncoercive Functionals, J. Differential Equations 127 (1996) 225-262. | MR 1387265 | Zbl 0856.49010

[8] Clarke F. H., An Indirect Method in the Calculus of Variations, Trans. Amer. Math. Soc. 336 (1993) 655-673. | MR 1118823 | Zbl 0780.49016

[9] Cupini G., Guidorzi M., Marcelli C., Necessary Conditions and Non-Existence Results for Autonomous Nonconvex Variational Problems, J. Differential Equations 243 (2007) 329-348. | MR 2371791 | Zbl 1168.49006

[10] G. Cupini, C. Marcelli, Monotonicity properties of minimizers and relaxation for autonomous variational problems, Università Politecnica delle Marche, preprint, 1, 2008.

[11] Dacorogna B., Introduction to the Calculus of Variations, Imperial College Press, London, 2004. | MR 2162819 | Zbl 1159.49001

[12] Fusco N., Marcellini P., Ornelas A., Existence of Minimizers for Some Non Convex One Dimensional Integrals, Portugal. Math. 55 (1998) 167-185. | MR 1629622 | Zbl 0912.49015

[13] Marcelli C., Variational Problems With Nonconvex, Noncoercive, Highly Discontinuous Integrands: Characterization and Existence of Minimizers, SIAM J. Control Optim. 40 (2002) 1473-1490. | MR 1882803 | Zbl 1030.49022

[14] Marcelli C., Necessary and Sufficient Conditions for Optimality of Nonconvex, Noncoercive Autonomous Variational Problems With Constraints, Trans. Amer. Math. Soc. 360 (2008) 5201-5227. | MR 2415071 | Zbl 1148.49025

[15] Marcellini P., Alcune Osservazioni Sull'esistenza Del Minimo Di Integrali Del Calcolo Delle Variazioni Senza Ipotesi Di Convessità, Rend. Mat. 13 (1980) 271-281. | Zbl 0454.49015

[16] Ornelas A., Existence of Scalar Minimizers for Nonconvex Simple Integrals of Sum Type, J. Math. Anal. Appl. 221 (1998) 559-573. | MR 1621754 | Zbl 0920.49026

[17] Raymond J. P., Existence and Uniqueness Results for Minimization Problems With Nonconvex Functionals, J. Optim. Theory Appl. 82 (1994) 571-592. | MR 1290664 | Zbl 0808.49002