On some nonlinear partial differential equations involving the “1”-laplacian and critical Sobolev exponent
ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 667-686.
@article{COCV_1999__4__667_0,
     author = {Demengel, Fran\c{c}oise},
     title = {On some nonlinear partial differential equations involving the {\textquotedblleft}1{\textquotedblright}-laplacian and critical {Sobolev} exponent},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {667--686},
     publisher = {EDP-Sciences},
     volume = {4},
     year = {1999},
     mrnumber = {1746172},
     zbl = {0939.35070},
     language = {en},
     url = {http://www.numdam.org/item/COCV_1999__4__667_0/}
}
TY  - JOUR
AU  - Demengel, Françoise
TI  - On some nonlinear partial differential equations involving the “1”-laplacian and critical Sobolev exponent
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 1999
SP  - 667
EP  - 686
VL  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/COCV_1999__4__667_0/
LA  - en
ID  - COCV_1999__4__667_0
ER  - 
%0 Journal Article
%A Demengel, Françoise
%T On some nonlinear partial differential equations involving the “1”-laplacian and critical Sobolev exponent
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 1999
%P 667-686
%V 4
%I EDP-Sciences
%U http://www.numdam.org/item/COCV_1999__4__667_0/
%G en
%F 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, Tome 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 | Zbl

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

[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 | Zbl

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

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

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

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

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

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

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