On a classical problem of the calculus of variations without convexity assumptions

A. Cellina; G. Colombo

doi:10.1016/s0294-1449(16)30306-7

JournalsaihpcVol. 7, No. 2pp. 97–106

On a classical problem of the calculus of variations without convexity assumptions

A. Cellina
S.I.S.S.A., I.S.A.S., Strada Costiera 11, 34014 Trieste, Italy
G. Colombo
S.I.S.S.A., I.S.A.S., Strada Costiera 11, 34014 Trieste, Italy

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Abstract

We show that the functional

I (x) = \int_{0}^{T} g (t, x (t)) d t + \int_{0}^{T} h (t, x' (t)) d t

attains a minimum under the condition that $g$ be concave in $x$ .

Résumé

Nous montrons que le fonctionnel

I (x) = \int_{0}^{T} g (t, x (t)) d t + \int_{0}^{T} h (t, x' (t)) d t

atteint le minimum sous la condition de concavité sur $g$ .

Cite this article

A. Cellina, G. Colombo, On a classical problem of the calculus of variations without convexity assumptions. Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), no. 2, pp. 97–106

DOI 10.1016/S0294-1449(16)30306-7