Minimizing a functional depending on u and on u
Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) no. 3, pp. 339-352.
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     author = {Cellina, Arrigo},
     title = {Minimizing a functional depending on $\nabla u$ and on $u$},
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     publisher = {Gauthier-Villars},
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     number = {3},
     year = {1997},
     zbl = {0876.49001},
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     url = {http://archive.numdam.org/item/AIHPC_1997__14_3_339_0/}
}
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Cellina, Arrigo. Minimizing a functional depending on $\nabla u$ and on $u$. Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997) no. 3, pp. 339-352. http://archive.numdam.org/item/AIHPC_1997__14_3_339_0/

[1] A. Cellina, On minima of a functional of the gradient: sufficient conditions, Nonlinear Analysis, TMA, Vol. 20, 1993, pp. 343-347. | MR | Zbl

[2] A. Cellina and S. Perrotta, On minima of radially symmetric functionals of the gradient, Nonlinear Analysis, TMA, Vol. 23, 1994, pp. 239-249. | MR | Zbl

[3] A. Cellina and S. Perrotta, On a problem of Potential Wells, Journal of Convex Anal.z, Vol. 2, 1995, pp. 103-116. | MR | Zbl

[4] A. Cellina and S. Zagatti, A version of Olech's Lemma in a Problem of the Calculus of Variations, SIAM J. Control and Optimization, Vol. 32, 1994, pp. 1114-1127. | MR | Zbl

[5] A. Cellina and S. Zagatti, An Existence Result in a Problem of the Vectorial Case of the Calculus of Variations, SIAM J. Control and Optimization, Vol. 333, 1995. | MR | Zbl

[6] B. Dacorogna and P. Marcellini, Existence of Minimizers for non quasiconvex integrals, Preprint Ecole Polytechnique Federale Lausanne, June 1994, to appear in: Arch. Rat. Mech. Anal. | MR | Zbl

[7] L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992. | MR | Zbl

[8] G. Friesecke, A necessary and sufficient condition for nonattainement and formation of microstructure almost everywhere in scalar variational problems, Proc. Royal Soc. Edinburgh, Vol. 124, 1984, pp. 437-471. | MR | Zbl

[9] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977. | MR | Zbl

[10] J. Goodman, V.R. Kohn and L. Reyna, Numerical study of a relaxed variational problem from optimal design, Computer Methods in Appl. Math. and Eng., Vol. 57, 1986, pp. 107-127. | MR | Zbl

[11] B. Kawohl, J. Stara and G. Wittum, Analysis and Numerical Studies of a Problem of Shape Design, Arch. Rat. Mech. Anal., Vol. 114, 1991, pp. 349-363. | MR | Zbl

[12] R.V. Kohn and G. Strang, Optimal Design and Relaxation of Variational Problems I, Comm. Pure Appl. Math., Vol. 39, 1986, pp. 113-137. | MR | Zbl

[13] E. Mascolo and R. Schianchi, Existence Theorems for Nonconvex Problems, J. Math. Pures Appl., Vol. 62, 1983, pp. 349-359. | MR | Zbl

[14] F. Murat and L. Tartar, Calcul des variations et Homegenization, in: Les Méthodes de l'homogenization, Eds: D. Bergman et al., Collection de la Direction des Études et recherche de l'Électricité de France, Vol. 57, 1985, pp. 319-369. | MR

[15] R. Tahraoui, Sur une classe de fonctionnelles non convexes et applications, SIAM J. Math. Anal., Vol. 21, 1990, pp. 37-52. | MR | Zbl

[16] R. Tahraoui, Théoremes d'existence en calcul des variations et applications a l'élasticité non lineaire, Proc. Royal Soc. Edinburgh, Vol. 109 A, 1988, pp. 51-78. | MR | Zbl