Radially symmetric solutions of a class of problems of the calculus of variations without convexity assumptions

Arrigo Cellina; Fabián Flores

doi:10.1016/s0294-1449(16)30235-9

JournalsaihpcVol. 9, No. 4pp. 465–477

Radially symmetric solutions of a class of problems of the calculus of variations without convexity assumptions

Arrigo Cellina
S.I.S.S.A., Strada Costiera 11, 34014 Trieste, Italy
Fabián Flores
S.I.S.S.A., Strada Costiera 11, 34014 Trieste, Italy

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Abstract

We show that the functional

I (u) = \int_{B} a (∣ x ∣) u (x) d x + \int_{B} h (∣ x ∣, Δ u (x) - λ u (x)) d x

attains a minimum on the space $W_{0}^{2, p} (B)$ .

Résumé

Nous montrons que le fonctionnel

I (u) = \int_{B} a (∣ x ∣) u (x) d x + \int_{B} h (∣ x ∣, Δ u (x) - λ u (x)) d x

atteint le minimum sur l’espace $W_{0}^{2, p} (B)$ .

Cite this article

Arrigo Cellina, Fabián Flores, Radially symmetric solutions of a class of problems of the calculus of variations without convexity assumptions. Ann. Inst. H. Poincaré Anal. Non Linéaire 9 (1992), no. 4, pp. 465–477

DOI 10.1016/S0294-1449(16)30235-9