Subcritical approximation of the Sobolev quotient and a related concentration result

Giampiero Palatucci

Rendiconti del Seminario Matematico della Università di Padova (2011)

  • Volume: 125, page 1-14
  • ISSN: 0041-8994

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Palatucci, Giampiero. "Subcritical approximation of the Sobolev quotient and a related concentration result." Rendiconti del Seminario Matematico della Università di Padova 125 (2011): 1-14. <http://eudml.org/doc/239991>.

@article{Palatucci2011,
author = {Palatucci, Giampiero},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {concentration of energy; critical Sobolev exponent},
language = {eng},
pages = {1-14},
publisher = {Seminario Matematico of the University of Padua},
title = {Subcritical approximation of the Sobolev quotient and a related concentration result},
url = {http://eudml.org/doc/239991},
volume = {125},
year = {2011},
}

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
PB - Seminario Matematico of the University of Padua
VL - 125
SP - 1
EP - 14
LA - eng
KW - concentration of energy; critical Sobolev exponent
UR - http://eudml.org/doc/239991
ER -

References

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  2. [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. Zbl0649.35033MR929280
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  4. [4] G. Dal Maso, An introduction to Γ -convergence, Birkhäuser, Boston, 1992. Zbl0816.49001MR1201152
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  6. [6] M. Flucher - S. Müller, Concentration of low extremals, Ann. Inst. H. Poincaré Anal. Non Linéaire, Vol. 10 (3) (1999), pp. 269–298. Zbl0938.35042
  7. [7] M. Flucher - A. Garroni - S. Müller, Concentration of low energy extremals: Identification of concentration points, Calc. Var., Vol. 14 (2002), pp. 483–516. Zbl1004.35040MR1911826
  8. [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. Zbl0729.35014MR1096602
  9. [9] J. Kazdan - F. Warner, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math., Vol. 38 (1975), pp. 557–569. Zbl0325.35038MR477445
  10. [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. Zbl0704.49005MR834360
  11. [11] G. Palatucci, p -Laplacian problems with critical Sobolev exponent, Asymptotic Analysis, to appear. Zbl1229.35101MR2841224
  12. [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. Zbl1296.35064
  13. [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. Zbl1066.35036MR2018666
  14. [14] S. Pohozaev, Eigenfunctions of the Equations Δ u = λ f ( u ) , Soviet Math. Dkl., Vol. 6 (1965), pp. 1408–1411. Zbl0141.30202
  15. [15] O. Rey, Proof of the conjecture of H. Brezis and L. A. Peletier, Manuscripta math., Vol. 65 (1989), pp. 19–37. Zbl0708.35032MR1006624

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