Stability results for some nonlinear elliptic equations involving the p -laplacian with critical Sobolev growth

Bruno Nazaret

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

  • Volume: 4, page 559-575
  • ISSN: 1292-8119

How to cite

top

Nazaret, Bruno. "Stability results for some nonlinear elliptic equations involving the $p$-laplacian with critical Sobolev growth." ESAIM: Control, Optimisation and Calculus of Variations 4 (1999): 559-575. <http://eudml.org/doc/90554>.

@article{Nazaret1999,
author = {Nazaret, Bruno},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {perturbation; viscosity term; best constant problem in Sobolev inequalities},
language = {eng},
pages = {559-575},
publisher = {EDP Sciences},
title = {Stability results for some nonlinear elliptic equations involving the $p$-laplacian with critical Sobolev growth},
url = {http://eudml.org/doc/90554},
volume = {4},
year = {1999},
}

TY - JOUR
AU - Nazaret, Bruno
TI - Stability results for some nonlinear elliptic equations involving the $p$-laplacian with critical Sobolev growth
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1999
PB - EDP Sciences
VL - 4
SP - 559
EP - 575
LA - eng
KW - perturbation; viscosity term; best constant problem in Sobolev inequalities
UR - http://eudml.org/doc/90554
ER -

References

top
  1. [1] T. Aubin, Problèmes isopérimétriques et espaces de Sobolev. J. Differential Geom. 11 ( 1976) 573-598. Zbl0371.46011MR448404
  2. [2] T. Aubin, Nonlinear Analysis on Manifolds. Monge-Ampere equations, Springer-Verlag ( 1982) (Grundlehren) 252. Zbl0512.53044MR681859
  3. [3] O. Druet, Generalized scalar curvature type equations on compact riemaniann manifolds. Preprint of the University of Cergy-Pontoise ( 1997). MR1649975
  4. [4] F. Demengel and E. Hebey, On some nonlinear equations involving the p-Laplacian with critical Sobolev growth. Adv. in PDE's, to appear. Zbl0955.35031MR1659246
  5. [5] P. Courilleau and F. Demengel, On the heat flow for p-harmonic maps with values in S1. Nonlinear Anal. TMA, accepted. Zbl0979.35082
  6. [6] M. Guedda and L. Veron, Local and global properties of solutions of quasilinear elliptic equations. J. Differential Equations 76 ( 1988) 159-189. Zbl0661.35029MR964617
  7. [7] M. Guedda and L. Veron, Quasilinear elliptic equations involving critical Sobolev exponentsNonlinear Analysis, Theory, Methods and Applications 13 ( 1989) 879-902. Zbl0714.35032MR1009077
  8. [8] 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
  9. [9] L.C. Evans, Weak convergence methods for nonlinear partial differential equations. Conference Board of the Mathematical Sciences 74 ( 1990). Zbl0698.35004MR1034481
  10. [10] E. Hebey, La methode d'isométries-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
  11. [11] E. Hebey, Sobolev Spaces on Riemannian Manifolds, Springer-Verlag ( 1996) (LNM) 1635. Zbl0866.58068MR1481970
  12. [12] A. Jourdain, Solutions nodales pour des équations de type courbure scalaire sur la sphère. Preprint of the University of Cergy-Pontoise ( 1997). 
  13. [13] P.L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, part I. Revista Matematica Iberoamericana 1 ( 1985) 145-199. Zbl0704.49005MR834360
  14. [14] P.L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, part II. Revista Matematica Iberoamericana 1 ( 1985) 45-116. Zbl0704.49006MR850686
  15. [15] B. Nazaret, Stabilité sous des perturbations visqueuses des solutions d'équations du type p-Laplacien avec exposant critique de Sobolev. Preprint of the University of Cergy-Pontoise (5/98). 
  16. [16] G. Talenti. Best constants in Sobolev inequalities. Ann. Mat. Pura Appl. 110 ( 1976) 353-372. Zbl0353.46018MR463908
  17. [17] P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations. J. Differential Equations 51 ( 1984) 126-150. Zbl0488.35017MR727034
  18. [18] J.L. Vazquez, A strong maximum principle for some quasilinear elliptic equations. Appl. Math. Optim. 12 ( 1984) 191-202. Zbl0561.35003MR768629

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.