Subcritical approximation of the Sobolev quotient and a related concentration result
Rendiconti del Seminario Matematico della Università di Padova, Tome 125 (2011), pp. 1-14. 
@article{RSMUP_2011__125__1_0,
     author = {Palatucci, Giampiero},
     title = {Subcritical approximation of the {Sobolev} quotient and a related concentration result},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {1--14},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {125},
     year = {2011},
     mrnumber = {2865956},
     zbl = {1234.35026},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2011__125__1_0/}
}
TY  - JOUR
AU  - Palatucci, Giampiero
TI  - Subcritical approximation of the Sobolev quotient and a related concentration result
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2011
SP  - 1
EP  - 14
VL  - 125
PB  - Seminario Matematico of the University of Padua
UR  - http://www.numdam.org/item/RSMUP_2011__125__1_0/
LA  - en
ID  - RSMUP_2011__125__1_0
ER  - 
%0 Journal Article
%A Palatucci, Giampiero
%T Subcritical approximation of the Sobolev quotient and a related concentration result
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2011
%P 1-14
%V 125
%I Seminario Matematico of the University of Padua
%U http://www.numdam.org/item/RSMUP_2011__125__1_0/
%G en
%F RSMUP_2011__125__1_0
Palatucci, Giampiero. Subcritical approximation of the Sobolev quotient and a related concentration result. Rendiconti del Seminario Matematico della Università di Padova, Tome 125 (2011), pp. 1-14. http://www.numdam.org/item/RSMUP_2011__125__1_0/

[1] M. Amar - A. Garroni, Γ -convergence of concentration problems, Ann. Scuola Norm. Sup. Pisa Cl. Sci., Vol. 2 (1) (2003), pp. 151-179. | Numdam | MR | Zbl

[2] A. Bahri - J. Coron, On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math., Vol. 41 (1988), pp. 253-294. | MR | Zbl

[3] H. Brezis - L. Peletier, Asymptotic for Elliptic Equations involving critical growth, Partial differential equations and the calculus of variations, Vol. I, Progr. Nonlinear Differential Equations Appl., Birkhäuser Boston, Boston, MA (1989), pp. 149-192. | MR | Zbl

[4] G. Dal Maso, An introduction to Γ -convergence, Birkhäuser, Boston, 1992. | MR | Zbl

[5] W. Ding, Positive solutions of Δu+u (n+2)/(n-2) =0 on a contractible domain, J. Partial Differential Equations, Vol. 2 (4) (1989), pp. 83-88. | MR | Zbl

[6] M. Flucher - S. Müller, Concentration of low extremals, Ann. Inst. H. Poincaré Anal. Non Linéaire, Vol. 10 (3) (1999), pp. 269-298. | Numdam | Zbl

[7] M. Flucher - A. Garroni - S. Müller, Concentration of low energy extremals: Identification of concentration points, Calc. Var., Vol. 14 (2002), pp. 483-516. | MR | Zbl

[8] Z. C. Han, Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent, Ann. Inst. Henri Poincaré, Vol. 8 (2) (1991), pp. 159-174. | Numdam | MR | Zbl

[9] J. Kazdan - F. Warner, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math., Vol. 38 (1975), pp. 557-569. | MR | Zbl

[10] P. L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, Rev. Mat. Iberoamericana, Vol. 1 (1985), pp. 145-201. | MR | Zbl

[11] G. Palatucci, p -Laplacian problems with critical Sobolev exponent, Asymptotic Analysis, to appear. | MR

[12] G. Palatucci - A. Pisante, Sobolev embeddings and concentration-compactness alternative for fractional Sobolev spaces, submitted paper, available online at http://mipa.unimes.fr/preprints.html.

[13] A. Pistoia - O. Rey, Boundary blow-up for a Brezis-Peletier problem on a singular domain, Calc. Var. Partial Differential Equations, Vol. 18 (3) (2003), 243-251. | MR | Zbl

[14] S. Pohozaev, Eigenfunctions of the Equations Δu=λf(u) , Soviet Math. Dkl., Vol. 6 (1965), pp. 1408-1411. | Zbl

[15] O. Rey, Proof of the conjecture of H. Brezis and L. A. Peletier, Manuscripta math., Vol. 65 (1989), pp. 19-37. | MR | Zbl