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, Volume 8 (1991) no. 2, p. 197-223
@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},
     publisher = {Gauthier-Villars},
     volume = {8},
     number = {2},
     year = {1991},
     pages = {197-223},
     zbl = {0729.49002},
     mrnumber = {1096604},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 8 (1991) no. 2, pp. 197-223. http://www.numdam.org/item/AIHPC_1991__8_2_197_0/

[1] M. Andersson, Optimal Foraging Area Size and Allocation of Search Effort, Theor. Popul. Biol., Vol. 13, 1978, pp. 397-409. | MR 503934

[2] R. Arditi and B. Dacorogna, Optimal Foraging in Non-Patchy Habitats. I. Bounded One-Dimensional Ressource, Math. Biosci., Vol. 76, 1985, pp. 127-145. | MR 813420 | Zbl 0577.92023

[3] R. Arditi and B. Dacorogna, 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 898834 | Zbl 0632.92023

[4] R. Arditi and B. Dacorogna, Optimal Foraging on Arbitrary Food Distributions and the Definition of Habitat Patches, Am. Nat., Vol. 131, 1988, pp. 837-846.

[5] J.M. Ball, Discontinuous Equilibrium Solutions and Cavitation in Nonlinear Elasticity, Phil. Trans. R. Soc. London, Vol. 306, 1982, pp. 557-611. | MR 703623 | Zbl 0513.73020

[6] J.M. Ball, Loss of the Constraint in Convex Variational Problems, in Analyse Mathématique et Applications, Gauthier-Villars, Paris, 1988, pp. 39-53. | MR 956952 | Zbl 0688.49005

[7] B. Botteron, Utilisations de méthodes d'optimisation en écologie, Mém. Soc. Vaud. Sc. Nat., Vol. 18.3, 1990, pp. 227-240.

[8] B. Botteron, Problèmes unidimensionnels non coercitifs du calcul des variations et applications en écologie, Ph. D. Thesis n° 845, École Polytechnique Fédérale de Lausanne, 1990.

[9] B. Botteron and R. Arditi, Central Place Foraging in Non-patchy Habitats (to appear). | Zbl 0781.92027

[10] B. Botteron and B. Dacorogna, 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 1044699 | Zbl 0717.49002

[11] B. Botteron and B. Dacorogna, Existence and Non-Existence Results for Non-Coercive Variational Problems and Applications in Ecology, J. Differential Equations, Vol. 85, 1990, pp. 214-235. | MR 1054549 | Zbl 0714.49002

[12] L. Cesari, Optimization Theory and Application, Springer, New York, 1983. | Zbl 0506.49001

[13] E.L. Charnov, Optimal Foraging Theory, the Marginal Value Theorem, Theor. Popul. Biol., Vol. 9, 1976, pp. 129-136. | Zbl 0334.92009

[14] J.N. Corvellec, Quelques remarques sur le problème de Lagrange du calcul des variations, Colloq. Math., Vol. 57, 1989, pp. 153-160. | MR 1028867 | Zbl 0703.49002

[15] B. Dacorogna, Direct Methods in the Calculus of Variations, Springer, New York, 1989. | MR 990890 | Zbl 0703.49001

[16] G. Dal Maso, Integral Representation on BV(Ω) of Γ-Limits of Variational Integrals, Manuscripta Math., Vol. 30, 1980, pp. 387-416. | MR 567216 | Zbl 0435.49016

[17] I. Ekeland and R. Temam, Analyse convexe et problème variationnels, Dunod, Paris, 1974. | MR 463993 | Zbl 0281.49001

[18] M. Giaquinta, G. Modica and J. Souček, Functionals with Linear Growth in the Calculus of Variations I, Commentationes Math. Univ. Carolinea, Vol. 20, 1979, pp. 143-172. | MR 526154 | Zbl 0421.49010

[19] E. Giusti, Non-Parametric Minimal Surfaces with Discontinuous and Thin Obstacles, Arch. Rational Mech. Anal., Vol. 49, 1972, pp. 41-56. | MR 346640 | Zbl 0257.49015

[20] A. Kacelnik and C. Bernstein, Optimal Foraging and Arbitrary Food Distributions: Patch Models Gain a Lease of Life, Trends Ecol. Evol., Vol. 3, 1988, pp. 251-253.

[21] J.R. Krebs and R.H. Mccleery, Optimization in Behavioural Ecology, in Behavioural Ecology, J. R. KREBS and N. B. DAVIES Eds., Blackwell, Oxford, 1984, pp. 91-121.

[22] H. Lebesgue, Intégrale, longueur, aire, Ann. Mat. Pura Appl., Vol. 7, 1902, pp. 231- 359. | JFM 33.0307.02

[23] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. | MR 259693 | Zbl 0189.40603

[24] P. Marcellini, 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 868523 | Zbl 0609.49009

[25] P. Marcellini, 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 969900 | Zbl 0667.49032

[26] P. Marcellini, 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 1034028 | Zbl 0679.73006

[27] M. Miranda, 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 181918 | Zbl 0137.08201

[28] C.B. Morrey, Multiple Integrals in the Calculus of Variations, D. Grundl. Math. Wiss., Vol. 130, Springer-Verlag, 1966. | MR 202511 | Zbl 0142.38701

[29] G.H. Pyke, Optimal Foraging Theory: A Critical Review, Annu. Rev. Ecol. Syst., Vol. 15, 1984, pp. 523-575.

[30] J. Serrin, On the Definition and Properties of Certain Variational Integrals, Trans. Am. Math. Soc., Vol. 101, 1961, pp. 139-167. | MR 138018 | Zbl 0102.04601

[31] R. Sibly and D. Mcfarland, On the Fitness of Behavior Sequences, Am. Nat., Vol. 110, 1976, pp. 601-617.

[32] L. Tonelli, Fondamenti di calcolo delle variazioni, Volume secondo, Zanichelli, Bologna, 1923. | JFM 50.0340.03

[33] L. Tonelli, Sulla quadratura delle superficie, Rendiconti Reale Accademia Nazionale Lincei, Vol. III, 1926, pp. 357-362, 445-450 and 633-638. | JFM 52.0251.01