The Euler Lagrange Equation and the Pontriagin Maximum Principle

Arrigo Cellina

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 2, page 323-347
  • ISSN: 0392-4041

Abstract

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We consider the necessary conditions in the Calculus of Variations, expressed by the validity of the Euler Lagrange equation, or of the Pontriagin Maximum Principle; in particular, problems on multi-dimensional domanis are considered.

How to cite

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Cellina, Arrigo. "The Euler Lagrange Equation and the Pontriagin Maximum Principle." Bollettino dell'Unione Matematica Italiana 8-B.2 (2005): 323-347. <http://eudml.org/doc/195819>.

@article{Cellina2005,
abstract = {We consider the necessary conditions in the Calculus of Variations, expressed by the validity of the Euler Lagrange equation, or of the Pontriagin Maximum Principle; in particular, problems on multi-dimensional domanis are considered.},
author = {Cellina, Arrigo},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {323-347},
publisher = {Unione Matematica Italiana},
title = {The Euler Lagrange Equation and the Pontriagin Maximum Principle},
url = {http://eudml.org/doc/195819},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Cellina, Arrigo
TI - The Euler Lagrange Equation and the Pontriagin Maximum Principle
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/6//
PB - Unione Matematica Italiana
VL - 8-B
IS - 2
SP - 323
EP - 347
AB - We consider the necessary conditions in the Calculus of Variations, expressed by the validity of the Euler Lagrange equation, or of the Pontriagin Maximum Principle; in particular, problems on multi-dimensional domanis are considered.
LA - eng
UR - http://eudml.org/doc/195819
ER -

References

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  2. BOUCHITTÉ, G., Lectures on Optimal Transportation, Cortona, August 2004. 
  3. BREZIS, H., Multiplicateur de Lagrange en torsion elasto-plastique, Arch. Rat. Mech. Anal. (1973), 32-40. Zbl0265.35021MR346346
  4. BREZIS, H. - SIBONY, M., Equivalence de deux inequations variationelles et applications, Arch. Rat. Mech. Anal., 41 (1971), 254-265. Zbl0214.11104MR346345
  5. CELADA, P. - CELLINA, A., Existence and non existence of solutions to a variational problem on a square, Houston J. of Math., 24 (1998), 345-375. Zbl0980.49020MR1690397
  6. CELLINA, A., Minimizing a functional depending on u and u , Ann. Inst. H. Poincaré, Anal. Non Lineaire, 14 (1997), 339-352. Zbl0876.49001MR1450952
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  8. CELLINA, A., On the validity of the Euler Lagrange equation, Jour. Diff. Equat., 171 (2001), 430-442. Zbl1015.49018MR1818657
  9. CELLINA, A., On a constrained Dirichlet problem, SIAM J. Control Optim., 41 (2002), 331-344. Zbl1055.49013MR1920261
  10. CELLINA, A. - PERROTTA, S., 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. Zbl0926.49014MR1638928
  11. CELLINA, A. - VORNICESCU, M., On gradient flows, Jour. Diff. Equat., 145 (1998), 489-501. Zbl0927.37007MR1620979
  12. CLARKE, F., Optimization and non smooth analysis, Wiley-Interscience, New York, 1983. 
  13. FERRIERO, A. - MARCHINI, E. M., On the validity of the Euler Lagrange equation, a preprint. Zbl1110.49019MR2124667
  14. PONTRIAGIN, L. - BOLTYIANSKII, V. - GAMKRELIDZE, R. - MISHCHENKO, E., The Mathematical Theory of Control Processes, Interscience, New York, 1962. 
  15. VORNICESCU, M., A variational Problem on subsets of R N , Proc. Royal. Soc. Edinburgh Sect. A, 127 (1997), 1089-1101. Zbl0920.49002MR1475648

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