Tower of bubbles for almost critical problems in general domains

Journal des Mathematiques Pures et Appliquees

Volumn 93, Issue 1, 2010, Pages 1-40

  Musso, Monica ^a   Pistoia, Angela ^b  

^a PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Blowing up solution; Critical Sobolev exponent; Robin's function; Tower of bubbles

Indexed keywords

EID: 73049092939     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2009.08.001     Document Type: Article

References (19)

1. Aubin T. Problèmes isopérimétriques et espaces de Sobolev. J. Differential Geometry 11 4 (1976) 573-598
2. Bianchi E., and Egnell H. A note on the Sobolev inequality. J. Funct. Anal. 100 (1991) 18-24
3. Brezis H., and Nirenberg L. Positive solutions of non-linear elliptic equations involving critical Sobolev exponents. Comm. Pure Appl. Math. 36 4 (1983) 437-477
4. Brezis H., and Peletier L.A. Asymptotics for elliptic equations involving critical growth. Partial Differential Equations and the Calculus of Variations, vol. I. Progr. Nonlinear Differential Equations Appl. vol. 1 (1989), Birkhäuser, Boston 149-192
5. del Pino M., Dolbeault J., and Musso M. "Bubble-tower" radial solutions in the slightly supercritical Brezis-Nirenberg problem. J. Differential Equations 193 2 (2003) 280-306
6. del Pino M., Dolbeault J., and Musso M. The Brezis-Nirenberg problem near criticality in dimension 3. J. Math. Pures Appl. (9) 83 12 (2004) 1405-1456
7. del Pino M., Felmer P., and Musso M. Two-bubble solutions in the supercritical Bahri-Coron problem. Calc. Var. Partial Differential Equations 16 2 (2003) 113-145
8. del Pino M., Musso M., and Pistoia A. Supercritical boundary bubbling in a semilinear Neumann problem. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 1 (2005) 45-82
9. Floer A., and Weinstein A. Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential. J. Funct. Anal. 69 3 (1986) 397-408
10. Ge Y., Jing R., and Pacard F. Bubble towers for supercritical semilinear elliptic equations. J. Funct. Anal. 221 2 (2005) 251-302
11. Grossi M. On the nondegeneracy of the critical points of the Robin function in symmetric domains. C. R. Acad. Sci. Paris 335 (2002) 1-4
12. Han Z.-C. Asymptotic approach to singular solutions for non-linear elliptic equations involving critical Sobolev exponent. Ann. Inst. H. Poincaré Anal. Non Linéaire 8 2 (1991) 159-174
13. Mazzeo R., and Pacard F. Constant scalar curvature metrics with isolated singularities. Duke Math. J. 99 3 (1999) 353-418
14. n. Nonlinear Anal. 52 1 (2003) 173-195
15. Molle R., and Pistoia A. Concentration phenomena in elliptic problems with critical and supercritical growth. Adv. Differential Equations 8 5 (2003) 547-570
16. Pistoia A., and Weth T. Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 2 (2007) 325-340
17. Pokhozhaev S.I. Eigenfunctions of the equation Δ u + λ f (u) = 0. Dokl. Akad. Nauk SSSR 165 (1965) 36-39
18. Rey O. The role of the Green's function in a non-linear elliptic equation involving the critical Sobolev exponent. J. Funct. Anal. 89 1 (1990) 1-52
19. Talenti G. Best constant in Sobolev inequality. Ann. Mat. Pura Appl. (IV) 110 (1976) 353-372