Geodesic
On Necessary Conditions in the Calculus of Variations
Publications de l'Institut Mathématique, _N_S_61 (1997) no. 75, p. 61 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Voir la notice de l'article

We consider weak and strong local solutions of the general isoperimetric problem. That problem differs from the classical calculus of variations in the fact that among constraints both constraints of the equality and of the inequality type appear. Necessary conditions (for both types of local solutions) are obtained, with no assumptions on integrand's phase variable. In the case of the simplest problem of calculus of variations necessary condition for $\hat x (\cdot)$ to be the weak local solution reduces here to the following equation $ {d\over dt} [\hat L_{\dot x} (t)\dot{\hat x} (t) (t) -\hat L (t)] =\hat L_t (t),\quad t\in [t_0, t_1], $ and necessary condition for $\hat x (\cdot)$ to be the strong local solution reduces here to the above differential equation together with the Weierstrass inequality.
Classification : 49B10
Keywords: isoperimetric problem, weak local minimum, strong local minimum, Lagrange multipliers. 
@article{PIM_1997_N_S_61_75_a8,
     author = {Vladimir Jankovi\'c},
     title = {On {Necessary} {Conditions} in the {Calculus} of {Variations}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {61 },
     year = {1997},
     volume = {_N_S_61},
     number = {75},
     zbl = {0946.49014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1997_N_S_61_75_a8/}
}
TY  - JOUR
AU  - Vladimir Janković
TI  - On Necessary Conditions in the Calculus of Variations
JO  - Publications de l'Institut Mathématique
PY  - 1997
SP  - 61 
VL  - _N_S_61
IS  - 75
UR  - http://geodesic.mathdoc.fr/item/PIM_1997_N_S_61_75_a8/
LA  - en
ID  - PIM_1997_N_S_61_75_a8
ER  - 
%0 Journal Article
%A Vladimir Janković
%T On Necessary Conditions in the Calculus of Variations
%J Publications de l'Institut Mathématique
%D 1997
%P 61 
%V _N_S_61
%N 75
%U http://geodesic.mathdoc.fr/item/PIM_1997_N_S_61_75_a8/
%G en
%F PIM_1997_N_S_61_75_a8
Vladimir Janković. On Necessary Conditions in the Calculus of Variations. Publications de l'Institut Mathématique, _N_S_61 (1997) no. 75, p. 61 . http://geodesic.mathdoc.fr/item/PIM_1997_N_S_61_75_a8/