On some nonlinear partial differential equations involving the “1”-laplacian and critical Sobolev exponent

Françoise Demengel

ESAIM: Control, Optimisation and Calculus of Variations (1999)

  • Volume: 4, page 667-686
  • ISSN: 1292-8119

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Demengel, Françoise. "On some nonlinear partial differential equations involving the “1”-laplacian and critical Sobolev exponent." ESAIM: Control, Optimisation and Calculus of Variations 4 (1999): 667-686. <http://eudml.org/doc/90560>.

@article{Demengel1999,
author = {Demengel, Françoise},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {1-Laplacian; critical Sobolev exponent; existence},
language = {eng},
pages = {667-686},
publisher = {EDP Sciences},
title = {On some nonlinear partial differential equations involving the “1”-laplacian and critical Sobolev exponent},
url = {http://eudml.org/doc/90560},
volume = {4},
year = {1999},
}

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
PB - EDP Sciences
VL - 4
SP - 667
EP - 686
LA - eng
KW - 1-Laplacian; critical Sobolev exponent; existence
UR - http://eudml.org/doc/90560
ER -

References

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  2. [2] T. Aubin, Nonlinear Analysis on manifolds-Monge-Ampère Equations. Grundlehern der Mathematischen Wissenschaften ( 1982) 252. Zbl0512.53044MR681859
  3. [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. Zbl0649.35033MR929280
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  5. [5] F. Demengel, Some compactness result for some spaces of functions with bounded derivatives. Arch. Rational Mech. Anal. 105 ( 1989) 123-161. Zbl0669.73030MR968458
  6. [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. Zbl0955.35031MR1659246
  7. [7] I. Ekeland and R. Temam, Convex Analysis and variational problems. North-Holland ( 1976). Zbl0322.90046MR463994
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  9. [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. Zbl0756.35028MR1154371
  10. [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. Zbl0798.35052MR1261094
  11. [11] P.L. Lions, La méthode de compacité concentration, I et II. Revista Ibero Americana 1 ( 1985) 145. Zbl0704.49005
  12. [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. Zbl0532.73039MR701898
  13. [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. Zbl0930.35051MR1746167
  14. [14] Talenti, Best constants in Sobolev inequality. Ann. Mat. Pura Appl. (4) 110 ( 1976) 353-372. Zbl0353.46018MR463908
  15. [15] G. Strang and R. Temam, Functions with bounded variations. Arch. Rational Mech. Anal. ( 1980) 493-527. Zbl0465.73033MR592100
  16. [16] P. Suquet, Sur les équations de la plasticité. Ann. Fac. Sci. Toulouse Math. (6) 1 ( 1979) 77-87. Zbl0405.46027MR533600
  17. [17] Ziemmer, Weakly Differentiable functions. Springer Verlag, Lectures Notes in Math. 120 ( 1989). Zbl0692.46022MR1014685

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