Nonoccurrence of the Lavrentiev phenomenon for nonconvex variational problems
Annales de l'I.H.P. Analyse non linéaire, Volume 22 (2005) no. 5, p. 579-596
@article{AIHPC_2005__22_5_579_0,
     author = {Zaslavski, Alexander J.},
     title = {Nonoccurrence of the Lavrentiev phenomenon for nonconvex variational problems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {22},
     number = {5},
     year = {2005},
     pages = {579-596},
     doi = {10.1016/j.anihpc.2004.10.004},
     zbl = {1098.49008},
     mrnumber = {2171992},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2005__22_5_579_0}
}
Zaslavski, Alexander J. Nonoccurrence of the Lavrentiev phenomenon for nonconvex variational problems. Annales de l'I.H.P. Analyse non linéaire, Volume 22 (2005) no. 5, pp. 579-596. doi : 10.1016/j.anihpc.2004.10.004. http://www.numdam.org/item/AIHPC_2005__22_5_579_0/

[1] Alberti G., Serra Cassano F., Non-occurrence of gap for one-dimensional autonomous functionals, in: Calculus of Variations, Homogenization and Continuum Mechanics (Marseille, 1993), Ser. Adv. Math. Appl. Sci., vol. 18, World Sci., River Edge, NJ, 1994, pp. 1-17. | MR 1428688 | Zbl 0884.49009

[2] Angell T.S., A note on the approximation of optimal solutions of the calculus of variations, Rend. Circ. Mat. Palermo 2 (1979) 258-272. | MR 580263 | Zbl 0445.49006

[3] Ball J.M., Mizel V.J., Singular minimizers for regular one-dimensional problems in the calculus of variations, Bull. Amer. Math. Soc. 11 (1984) 143-146. | MR 741726 | Zbl 0541.49010

[4] Ball J.M., Mizel V.J., One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation, Arch. Rational Mech. Anal. 90 (1985) 325-388. | MR 801585 | Zbl 0585.49002

[5] Brezis H., Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert, North-Holland, Amsterdam, 1973. | MR 348562 | Zbl 0252.47055

[6] Cesari L., Optimization - Theory and Applications, Springer-Verlag, Berlin, 1983. | MR 688142 | Zbl 0506.49001

[7] Clarke F.H., Vinter R.B., Regularity properties of solutions to the basic problem in the calculus of variations, Trans. Amer. Math. Soc. 289 (1985) 73-98. | MR 779053 | Zbl 0563.49009

[8] Clarke F.H., Vinter R.B., Regularity of solutions to variational problems with polynomial Lagrangians, Bull. Polish Acad. Sci. 34 (1986) 73-81. | MR 850317 | Zbl 0598.49013

[9] Lavrentiev M., Sur quelques problemes du calcul des variations, Ann. Math. Pura Appl. 4 (1926) 107-124. | JFM 53.0481.02 | MR 1553097

[10] Loewen P.D., On the Lavrentiev phenomenon, Canad. Math. Bull. 30 (1987) 102-108. | MR 879878 | Zbl 0579.49002

[11] Mania B., Sopra un esempio di Lavrentieff, Boll. Un. Mat. Ital. 13 (1934) 146-153. | Zbl 0009.15803

[12] Sychev M.A., Mizel V.J., A condition on the value function both necessary and sufficient for full regularity of minimizers of one-dimensional variational problems, Trans. Amer. Math. Soc. 350 (1998) 119-133. | MR 1357405 | Zbl 0888.49028