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.
Si esaminano le condizioni necessarie del Calcolo delle Variazioni, espresse sotto la forma dell'equazione di Eulero Lagrange e del Principio del Massimo di Pontriagin; in particolare, si esaminano i problemi su domini multi-dimensionali.
@article{BUMI_2005_8_8B_2_323_0, author = {Arrigo Cellina}, title = {The Euler Lagrange Equation and the Pontriagin Maximum Principle}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {8-A}, year = {2005}, pages = {323-347}, zbl = {1178.49021}, mrnumber = {2149387}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2005_8_8B_2_323_0} }
Cellina, Arrigo. The Euler Lagrange Equation and the Pontriagin Maximum Principle. Bollettino dell'Unione Matematica Italiana, Tome 8-A (2005) pp. 323-347. http://gdmltest.u-ga.fr/item/BUMI_2005_8_8B_2_323_0/
[1] One dimensional minimum problems whose minimizers do not satisfy the Euler Lagrange equation, Arch. Rat. Mech. Anal., 90 (1985), 325-388 | MR 801585 | Zbl 0585.49002
- ,[2] Lectures on Optimal Transportation, Cortona, August 2004.
,[3] Multiplicateur de Lagrange en torsion elasto-plastique, Arch. Rat. Mech. Anal. (1973), 32-40. | MR 346346 | Zbl 0265.35021
,[4] Equivalence de deux inequations variationelles et applications, Arch. Rat. Mech. Anal., 41 (1971), 254-265. | MR 346345 | Zbl 0214.11104
- ,[5] Existence and non existence of solutions to a variational problem on a square, Houston J. of Math., 24 (1998), 345-375. | MR 1690397 | Zbl 0980.49020
- ,[6] Minimizing a functional depending on and , Ann. Inst. H. Poincaré, Anal. Non Lineaire, 14 (1997), 339-352. | MR 1450952 | Zbl 0876.49001
,[7] On uniqueness almost everywhere for monotonic differential inclusions, Nonlinear Analysis TMA, 25 (1995), 899-903. | MR 1350714 | Zbl 0837.34023
,[8] On the validity of the Euler Lagrange equation, Jour. Diff. Equat., 171 (2001), 430-442. | MR 1818657 | Zbl 1015.49018
,[9] On a constrained Dirichlet problem, SIAM J. Control Optim., 41 (2002), 331-344. | MR 1920261 | Zbl 1055.49013
,[10] 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. | MR 1638928 | Zbl 0926.49014
- ,[11] On gradient flows, Jour. Diff. Equat., 145 (1998), 489-501. | MR 1620979 | Zbl 0927.37007
- ,[12]
, Optimization and non smooth analysis, Wiley-Interscience, New York, 1983.[13] On the validity of the Euler Lagrange equation, a preprint. | MR 2124667 | Zbl 1110.49019
- ,[14]
- - - , The Mathematical Theory of Control Processes, Interscience, New York, 1962.[15] A variational Problem on subsets of , Proc. Royal. Soc. Edinburgh Sect. A, 127 (1997), 1089-1101. | MR 1475648 | Zbl 0920.49002
,