On some nonlinear partial differential equations involving the “1”-laplacian and critical Sobolev exponent
ESAIM: Control, Optimisation and Calculus of Variations, Volume 4 (1999), p. 667-686
@article{COCV_1999__4__667_0,
     author = {Demengel, Fran\c coise},
     title = {On some nonlinear partial differential equations involving the ``1''-laplacian and critical Sobolev exponent},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {4},
     year = {1999},
     pages = {667-686},
     zbl = {0939.35070},
     mrnumber = {1746172},
     language = {en},
     url = {http://www.numdam.org/item/COCV_1999__4__667_0}
}
Demengel, Françoise. On some nonlinear partial differential equations involving the “1”-laplacian and critical Sobolev exponent. ESAIM: Control, Optimisation and Calculus of Variations, Volume 4 (1999) pp. 667-686. http://www.numdam.org/item/COCV_1999__4__667_0/

[1] T. Aubin, Problèmes isopérimétriques et espaces de Sobolev. J. Differential Geom. 11 ( 1976) 573-598. | MR 448404 | Zbl 0371.46011

[2] T. Aubin, Nonlinear Analysis on manifolds-Monge-Ampère Equations. Grundlehern der Mathematischen Wissenschaften ( 1982) 252. | MR 681859 | Zbl 0512.53044

[3] A. Bahri and J.M. Coron, On a non linear elliptic equation involving the critical Sobolev exponent: The effet of the topology of the domain. Comm. Pure Appl. Math. 41 ( 1988) 253-294. | MR 929280 | Zbl 0649.35033

[4] Bobkov and Ch. Houdré, Some connections between isoperimetric and Sobolev type Inequalities. Mem. Amer. Math. Soc. 616 ( 1997). | MR 1396954 | Zbl 0886.49033

[5] F. Demengel, Some compactness result for some spaces of functions with bounded derivatives. Arch. Rational Mech. Anal. 105 ( 1989) 123-161. | MR 968458 | Zbl 0669.73030

[6] F. Demengel and E. Hebey, On some nonlinear equations involving the p-Laplacian with critical Sobolev growth. I. Adv. Partial Differential Equations 3 ( 1998) 533-574. | MR 1659246 | Zbl 0955.35031

[7] I. Ekeland and R. Temam, Convex Analysis and variational problems. North-Holland ( 1976). | MR 463994 | Zbl 0322.90046

[8] E. Giusti, Minimal surfaces and functions of bounded variation, notes de cours rédigés par G.H. Williams. Department of Mathematics Australian National University, Canberra ( 1977), et Birkhaiiser ( 1984). | MR 638362 | Zbl 0402.49033

[9] E. Hebey, La méthode d'isométrie concentration dans le cas d'un problème non linéaire sur les variétés compactes à bord avec exposant critique de Sobolev. Bull. Sci. Math. 116 ( 1992) 35-51. | MR 1154371 | Zbl 0756.35028

[10] E. Hebey and M. Vaugon, Existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical Sobolev Growth. J. Funct. Anal. 119 ( 1994) 298-318. | MR 1261094 | Zbl 0798.35052

[11] P.L. Lions, La méthode de compacité concentration, I et II. Revista Ibero Americana 1 ( 1985) 145. | Zbl 0704.49005

[12] R.V. Kohn and R. Temam, Dual spaces of stress and strains with applications to Hencky plasticity. Appl. Math. Optim. 10 ( 1983) 1-35. | MR 701898 | Zbl 0532.73039

[13] B. Nazaret, Stability results for some nonlinear elliptic equations involving the p-Laplacian with critical Sobolev growth, COCV, accepted Version française : Prepublication de l'Université de Cergy-Pontoise N 5/98, Avril 1998. | Numdam | MR 1746167 | Zbl 0930.35051

[14] Talenti, Best constants in Sobolev inequality. Ann. Mat. Pura Appl. (4) 110 ( 1976) 353-372. | MR 463908 | Zbl 0353.46018

[15] G. Strang and R. Temam, Functions with bounded variations. Arch. Rational Mech. Anal. ( 1980) 493-527. | MR 592100 | Zbl 0465.73033

[16] P. Suquet, Sur les équations de la plasticité. Ann. Fac. Sci. Toulouse Math. (6) 1 ( 1979) 77-87. | Numdam | MR 533600 | Zbl 0405.46027

[17] Ziemmer, Weakly Differentiable functions. Springer Verlag, Lectures Notes in Math. 120 ( 1989). | MR 1014685 | Zbl 0692.46022