PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1992 | 27 | 2 | 383-397
Tytuł artykułu

Elliptic equations with limiting Sobolev exponent: the impact of the Green's function

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
27
Numer
2
Strony
383-397
Opis fizyczny
Daty
wydano
1992
Twórcy
autor
  • Centre de Mathématiques, Ecole Polytechnique, F-91128 Palaiseau, France
Bibliografia
  • [1] T. Aubin, Problèmes isopérimétriques et espaces de Sobolev, J. Differential Geom. 11 (1976), 573-598.
  • [2] T. Aubin, Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, J. Math. Pures Appl. 55 (1976), 269-296.
  • [3] A. Bahri, Critical Points at Infinity in Some Variational Problems, Pitman Res. Notes Math. Ser. 182, Longman, 1989.
  • [4] A. Bahri et J. M. Coron, Vers une théorie des points critiques à l'infini, Séminaire EDP Ecole Polytechnique 1984-1985, n°8.
  • [5] A. Bahri et J. M. Coron, Sur une équation elliptique non linéaire avec l'exposant critique de Sobolev, C. R. Acad. Sci. Paris Sér. I 301 (1985), 345-348.
  • [6] A. Bahri et J. M. Coron, On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math. 41 (1988), 255-294.
  • [7] A. Bahri, Y. Li and O. Rey, On a variational problem with lack of compactness. The topological effect of the critical points at infinity, to appear.
  • [8] H. Brézis and J. M. Coron, Convergence of solutions of H-systems or how to blow bubbles, Arch. Rational Mech. Anal. 89 (1985), 21-56.
  • [9] H. Brézis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 437-477.
  • [10] H. Brézis and L. A. Peletier, Asymptotics for elliptic equations involving the critical growth, in: Partial Differential Equations and the Calculus of Variations, F. Colombani and S. % Spagnolo (eds.), Birkhäuser, 1989.
  • [11] J. M. Coron, Topologie et cas limite des injections de Sobolev, C. R. Acad. Sci. Paris Sér. I 299 (1984), 209-212.
  • [12] E. N. Dancer, A note on an equation with critical exponent, Bull. London Math. Soc. 20 (1988), 600-602.
  • [13] W. Y. Ding, On a conformally invariant elliptic equation on $ℝ^n$, Comm. Math. Phys. 107 (1986), 331-335.
  • [14] W. Y. Ding, Positive solutions of $∆u + u^{(n+2)/(n-2)} = 0$ on contractible domains, to appear.
  • [15] B. Gidas, Symmetry properties and isolated singularities of positive solutions of nonlinear elliptic equations, in: Nonlinear Partial Differential Equations in Engineering and Applied Science, Sternberg et al. (eds.), Dekker, New York 1980, 255-273.
  • [16] B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in $ℝ^n$, in: Mathematical Analysis and Applications, Part A, L. Nachbin (ed.), Academic Press, 1981, 370-402.
  • [17] Z. C. Han, Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent, Ann. Inst. Poincaré Anal. Non Linéaire 8 (1991), 159-174.
  • [18] J. Kazdan, Prescribing the Curvature of a Riemannian Manifold, CBMS Regional Conf. Ser. in Math. 57, Amer. Math. Soc., 1985.
  • [19] E. Lieb, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. of Math. 118 (1983), 349-374.
  • [20] P. L. Lions, The concentration-compactness principle in the Calculus of Variations. The locally compact case. Parts 1 and 2, Ann. Inst. Poincaré Anal. Non Linéaire 1 (1984), 109-145 and 223-284.
  • [21] P. L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, Rev. Mat. Iberoamericana 1(1) (1985), 145-201, and 1(2) (1985), 45-121.
  • M. Obata, The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geom. 6 (1971), 247-258.
  • [23] S. I. Pokhozhaev, Eigenfunctions of the equation ∆u + λf(u) = 0, Soviet Math. Dokl. 6 (1965), 1408-1411.
  • [24] O. Rey, The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal. 89 (1990), 1-52.
  • [25] O. Rey, Sur un problème variationnel non compact: l'effet de petits trous dans le domaine, C. R. Acad. Sci. Paris Sér. I 308 (1989), 349-352.
  • [26] O. Rey, The proof of two conjectures of H. Brézis and L. A. Peletier, Manuscripta Math. 65 (1989), 19-37.
  • [27] O. Rey, Blow-up points of solutions to elliptic equations with limiting non linearity, Differential and Integral Equations, to appear.
  • [28] R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984), 479-495.
  • [29] R. Schoen, in preparation.
  • [30] M. Struwe, A global compactness result for elliptic boundary value problems involving limiting nonlinearities, Math. Z. 187 (1984), 511-517.
  • [31] G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976), 353-372.
  • [32] N. Trudinger, Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa 22 (1968), 265-274.
  • [33] H. Yamabe, On a deformation of Riemannian structures on compact manifolds, Osaka Math. J. 12 (1960), 21-37.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv27z2p383bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.