@article{AIHPC_1991__8_2_197_0,
author = {Botteron, Bernard and Marcellini, Paolo},
title = {A general approach to the existence of minimizers of one-dimensional non-coercive integrals of the calculus of variations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {197--223},
publisher = {Gauthier-Villars},
volume = {8},
number = {2},
year = {1991},
mrnumber = {1096604},
zbl = {0729.49002},
language = {en},
url = {http://www.numdam.org/item/AIHPC_1991__8_2_197_0/}
}
TY - JOUR AU - Botteron, Bernard AU - Marcellini, Paolo TI - A general approach to the existence of minimizers of one-dimensional non-coercive integrals of the calculus of variations JO - Annales de l'I.H.P. Analyse non linéaire PY - 1991 SP - 197 EP - 223 VL - 8 IS - 2 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPC_1991__8_2_197_0/ LA - en ID - AIHPC_1991__8_2_197_0 ER -
%0 Journal Article %A Botteron, Bernard %A Marcellini, Paolo %T A general approach to the existence of minimizers of one-dimensional non-coercive integrals of the calculus of variations %J Annales de l'I.H.P. Analyse non linéaire %D 1991 %P 197-223 %V 8 %N 2 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPC_1991__8_2_197_0/ %G en %F AIHPC_1991__8_2_197_0
Botteron, Bernard; Marcellini, Paolo. A general approach to the existence of minimizers of one-dimensional non-coercive integrals of the calculus of variations. Annales de l'I.H.P. Analyse non linéaire, Tome 8 (1991) no. 2, pp. 197-223. http://www.numdam.org/item/AIHPC_1991__8_2_197_0/
[1] , Optimal Foraging Area Size and Allocation of Search Effort, Theor. Popul. Biol., Vol. 13, 1978, pp. 397-409. | MR
[2] and , Optimal Foraging in Non-Patchy Habitats. I. Bounded One-Dimensional Ressource, Math. Biosci., Vol. 76, 1985, pp. 127-145. | MR | Zbl
[3] and , Optimal Foraging in Non-patchy Habitats. II. Unbounded One-Dimensional Habitat, S.I.A.M. J. Appl. Math., Vol. 47, 1987, pp. 800-821. | MR | Zbl
[4] and , Optimal Foraging on Arbitrary Food Distributions and the Definition of Habitat Patches, Am. Nat., Vol. 131, 1988, pp. 837-846.
[5] , Discontinuous Equilibrium Solutions and Cavitation in Nonlinear Elasticity, Phil. Trans. R. Soc. London, Vol. 306, 1982, pp. 557-611. | MR | Zbl
[6] , Loss of the Constraint in Convex Variational Problems, in Analyse Mathématique et Applications, Gauthier-Villars, Paris, 1988, pp. 39-53. | MR | Zbl
[7] , Utilisations de méthodes d'optimisation en écologie, Mém. Soc. Vaud. Sc. Nat., Vol. 18.3, 1990, pp. 227-240.
[8] , Problèmes unidimensionnels non coercitifs du calcul des variations et applications en écologie, Ph. D. Thesis n° 845, École Polytechnique Fédérale de Lausanne, 1990.
[9] and , Central Place Foraging in Non-patchy Habitats (to appear). | Zbl
[10] and , Existence of Solutions for a Variational Problem Associated to Models in Optimal Foraging Theory, J. Math. Anal. Appl., Vol. 147, 1990, pp. 263-276. | MR | Zbl
[11] and , Existence and Non-Existence Results for Non-Coercive Variational Problems and Applications in Ecology, J. Differential Equations, Vol. 85, 1990, pp. 214-235. | MR | Zbl
[12] , Optimization Theory and Application, Springer, New York, 1983. | Zbl
[13] , Optimal Foraging Theory, the Marginal Value Theorem, Theor. Popul. Biol., Vol. 9, 1976, pp. 129-136. | Zbl
[14] , Quelques remarques sur le problème de Lagrange du calcul des variations, Colloq. Math., Vol. 57, 1989, pp. 153-160. | MR | Zbl
[15] , Direct Methods in the Calculus of Variations, Springer, New York, 1989. | MR | Zbl
[16] , Integral Representation on BV(Ω) of Γ-Limits of Variational Integrals, Manuscripta Math., Vol. 30, 1980, pp. 387-416. | MR | Zbl
[17] and , Analyse convexe et problème variationnels, Dunod, Paris, 1974. | MR | Zbl
[18] , and , Functionals with Linear Growth in the Calculus of Variations I, Commentationes Math. Univ. Carolinea, Vol. 20, 1979, pp. 143-172. | MR | Zbl
[19] , Non-Parametric Minimal Surfaces with Discontinuous and Thin Obstacles, Arch. Rational Mech. Anal., Vol. 49, 1972, pp. 41-56. | MR | Zbl
[20] and , Optimal Foraging and Arbitrary Food Distributions: Patch Models Gain a Lease of Life, Trends Ecol. Evol., Vol. 3, 1988, pp. 251-253.
[21] and , Optimization in Behavioural Ecology, in Behavioural Ecology, J. R. KREBS and N. B. DAVIES Eds., Blackwell, Oxford, 1984, pp. 91-121.
[22] , Intégrale, longueur, aire, Ann. Mat. Pura Appl., Vol. 7, 1902, pp. 231- 359. | JFM
[23] , Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. | MR | Zbl
[24] , On the Definition and the Lower Semicontinuity of Certain Quasiconvex Integrals, Ann. Inst. Henri-Poincaré, Analyse non Linéaire, Vol. 3, 1986, pp. 391- 409. | Numdam | MR | Zbl
[25] , Regularity of Minimizers of Integrals of the Calculus of Variations with Non Standard Growth Conditions, Arch. Rational. Mech. Anal., Vol. 105, 1989, pp. 267-284. | MR | Zbl
[26] , The Stored-Energy for Some Discontinuous Deformations in Nonlinear Elasticity, Essays in honor of E. De Giorgi, Partial Differential Eq. and the Calculus of Variations, Vol. II, A. COLOMBINI and Ed., Birkhäuser, 1989, pp. 767-786 | MR | Zbl
[27] , Un teorema di esistenza e unicità per il problema dell' area minima in n variabili, Ann. Scuola Norm. Sup. Pisa, Vol. 19, 1965, p. 233-249. | Numdam | MR | Zbl
[28] , Multiple Integrals in the Calculus of Variations, D. Grundl. Math. Wiss., Vol. 130, Springer-Verlag, 1966. | MR | Zbl
[29] , Optimal Foraging Theory: A Critical Review, Annu. Rev. Ecol. Syst., Vol. 15, 1984, pp. 523-575.
[30] , On the Definition and Properties of Certain Variational Integrals, Trans. Am. Math. Soc., Vol. 101, 1961, pp. 139-167. | MR | Zbl
[31] and , On the Fitness of Behavior Sequences, Am. Nat., Vol. 110, 1976, pp. 601-617.
[32] , Fondamenti di calcolo delle variazioni, Volume secondo, Zanichelli, Bologna, 1923. | JFM
[33] , Sulla quadratura delle superficie, Rendiconti Reale Accademia Nazionale Lincei, Vol. III, 1926, pp. 357-362, 445-450 and 633-638. | JFM
