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

Abstract

We show that the functional

attains a minimum under the condition that be concave in .

Résumé

Nous montrons que le fonctionnel

atteint le minimum sous la condition de concavité sur .

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