Geodesic
Positive Solution of a Subelliptic Nonlinear Equation on the Heisenberg Group
Canadian mathematical bulletin, Tome 44 (2001) no. 3, pp. 346-354

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we establish the existence of positive solution of a nonlinear subelliptic equation involving the critical Sobolev exponent on the Heisenberg group, which generalizes a result of Brezis and Nirenberg in the Euclidean case.
DOI : 10.4153/CMB-2001-035-0
Mots-clés : 35J20, 35J60, Heisenberg group, subLapacian, critical Sobolev exponent, extremals 
Wang, Wei. Positive Solution of a Subelliptic Nonlinear Equation on the Heisenberg Group. Canadian mathematical bulletin, Tome 44 (2001) no. 3, pp. 346-354. doi: 10.4153/CMB-2001-035-0
@article{10_4153_CMB_2001_035_0,
     author = {Wang, Wei},
     title = {Positive {Solution} of a {Subelliptic} {Nonlinear} {Equation} on the {Heisenberg} {Group}},
     journal = {Canadian mathematical bulletin},
     pages = {346--354},
     year = {2001},
     volume = {44},
     number = {3},
     doi = {10.4153/CMB-2001-035-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-035-0/}
}
TY  - JOUR
AU  - Wang, Wei
TI  - Positive Solution of a Subelliptic Nonlinear Equation on the Heisenberg Group
JO  - Canadian mathematical bulletin
PY  - 2001
SP  - 346
EP  - 354
VL  - 44
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-035-0/
DO  - 10.4153/CMB-2001-035-0
ID  - 10_4153_CMB_2001_035_0
ER  - 
%0 Journal Article
%A Wang, Wei
%T Positive Solution of a Subelliptic Nonlinear Equation on the Heisenberg Group
%J Canadian mathematical bulletin
%D 2001
%P 346-354
%V 44
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-035-0/
%R 10.4153/CMB-2001-035-0
%F 10_4153_CMB_2001_035_0

[BN] [BN] Brezis, H. and Nirenberg, L., Positive solutions of nonlinear elliptic equation involving critical Sobolev exponents. Comm. Pure Appl. Math. 36 (1983), 437–477. Google Scholar

[CDG] [CDG] Capogna, L., Danielli, D. and Garofalo, N., An embedding theorem and the Harnark inequality for nonlinear subelliptic equations. Comm. Partial Differential Equations 18 (1993), 1765–1794. Google Scholar

[FS] [FS] Folland, G. B. and Stein, E. M., Estimates for the ∂b complex and analysis on the Heisenberg group. Comm. Pure Appl. Math. 27 (1974), 429–522. Google Scholar

[GL1] [GL1] Garofalo, N. and Lanconelli, E., Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation. Ann. Inst. Fourier Grenoble 40 (1990), 313–356. Google Scholar

[GL2] [GL2] Garofalo, N. and Lanconelli, E., Existence and nonexistence results for semilinear equations on the Heisenberg group. Indiana Univ.Math. J. (1) 41 (1992), 71–98. Google Scholar

[GT] [GT] Gilbarg, D. and Trudinger, N. S., Elliptic partial differential equations of second order. Grundlehren Math.Wiss. 224, Springer-Verlag, 1977. Google Scholar

[JL1] [JL1] Jerison, D. S. and Lee, L. M., Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem. J. Amer. Math. Soc. 1 (1988), 1–13. Google Scholar

[JL2] [JL2] Jerison, D. S. and Lee, L. M., Intrinsic CR coordinates and the CR Yamabe problem. J. Differential Geom. 29 (1989), 303–343. Google Scholar

[S] [S] Showalter, R. E., Hilbert space methods for partial differential equations. Pitman Publishing, London, 1977. Google Scholar

Cité par Sources :