Nonoccurrence of the Lavrentiev phenomenon for nonconvex variational problems

Alexander J. Zaslavski

Annales de l'I.H.P. Analyse non linéaire (2005)

  • Volume: 22, Issue: 5, page 579-596
  • ISSN: 0294-1449

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Zaslavski, Alexander J.. "Nonoccurrence of the Lavrentiev phenomenon for nonconvex variational problems." Annales de l'I.H.P. Analyse non linéaire 22.5 (2005): 579-596. <http://eudml.org/doc/78670>.

@article{Zaslavski2005,
author = {Zaslavski, Alexander J.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Lavrentiev phenomenon; Banach-valued functions; approximation in energy},
language = {eng},
number = {5},
pages = {579-596},
publisher = {Elsevier},
title = {Nonoccurrence of the Lavrentiev phenomenon for nonconvex variational problems},
url = {http://eudml.org/doc/78670},
volume = {22},
year = {2005},
}

TY - JOUR
AU - Zaslavski, Alexander J.
TI - Nonoccurrence of the Lavrentiev phenomenon for nonconvex variational problems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2005
PB - Elsevier
VL - 22
IS - 5
SP - 579
EP - 596
LA - eng
KW - Lavrentiev phenomenon; Banach-valued functions; approximation in energy
UR - http://eudml.org/doc/78670
ER -

References

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  1. [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. Zbl0884.49009MR1428688
  2. [2] Angell T.S., A note on the approximation of optimal solutions of the calculus of variations, Rend. Circ. Mat. Palermo2 (1979) 258-272. Zbl0445.49006MR580263
  3. [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. Zbl0541.49010MR741726
  4. [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. Zbl0585.49002MR801585
  5. [5] Brezis H., Opérateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert, North-Holland, Amsterdam, 1973. Zbl0252.47055MR348562
  6. [6] Cesari L., Optimization – Theory and Applications, Springer-Verlag, Berlin, 1983. Zbl0506.49001MR688142
  7. [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. Zbl0563.49009MR779053
  8. [8] Clarke F.H., Vinter R.B., Regularity of solutions to variational problems with polynomial Lagrangians, Bull. Polish Acad. Sci.34 (1986) 73-81. Zbl0598.49013MR850317
  9. [9] Lavrentiev M., Sur quelques problemes du calcul des variations, Ann. Math. Pura Appl.4 (1926) 107-124. JFM53.0481.02
  10. [10] Loewen P.D., On the Lavrentiev phenomenon, Canad. Math. Bull.30 (1987) 102-108. Zbl0579.49002MR879878
  11. [11] Mania B., Sopra un esempio di Lavrentieff, Boll. Un. Mat. Ital.13 (1934) 146-153. Zbl0009.15803
  12. [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. Zbl0888.49028MR1357405

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