On the Liouville property for sublaplacians
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 25 (1997) no. 1-2, pp. 239-256.
@article{ASNSP_1997_4_25_1-2_239_0,
     author = {Capuzzo Dolcetta, Italo and Cutr{\`\i}, Alessandra},
     title = {On the {Liouville} property for sublaplacians},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {239--256},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 25},
     number = {1-2},
     year = {1997},
     mrnumber = {1655517},
     zbl = {1042.35013},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1997_4_25_1-2_239_0/}
}
TY  - JOUR
AU  - Capuzzo Dolcetta, Italo
AU  - Cutrì, Alessandra
TI  - On the Liouville property for sublaplacians
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1997
SP  - 239
EP  - 256
VL  - 25
IS  - 1-2
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1997_4_25_1-2_239_0/
LA  - en
ID  - ASNSP_1997_4_25_1-2_239_0
ER  - 
%0 Journal Article
%A Capuzzo Dolcetta, Italo
%A Cutrì, Alessandra
%T On the Liouville property for sublaplacians
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1997
%P 239-256
%V 25
%N 1-2
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1997_4_25_1-2_239_0/
%G en
%F ASNSP_1997_4_25_1-2_239_0
Capuzzo Dolcetta, Italo; Cutrì, Alessandra. On the Liouville property for sublaplacians. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 25 (1997) no. 1-2, pp. 239-256. http://www.numdam.org/item/ASNSP_1997_4_25_1-2_239_0/

[1] H. Berestycki - I. Capuzzo Dolcetta - L. Nirenberg, Problèmes elliptiques indéfinis et théorèmes de Liouville non-linéaires, C. R. Acad. Sci. Paris, Série 1317 (1993), 945-950. | MR | Zbl

[2] H. Berestycki - I. Capuzzo Dolcetta - L. Nirenberg, Superlinear indefinite elliptic problems and nonlinear Liouville theorems, Topological Methods in Nonlinear Analysis 4,1 (1995) 59-78. | MR | Zbl

[3] S. Biagini, Positive solutions for a semilinear equation on the Heisenberg group, Bull. UMI 9, B (1995), 883-900. | MR | Zbl

[4] I. Birindelli, Nonlinear Liouville theorems, to appear in "Reaction Diffusion Systems", Caristi and Mitidieri (eds) | MR | Zbl

[5] I. Birindelli - I. Capuzzo Dolcetta - A. Cutri, Liouville theorems for semilinear equations on the Heisenberg group, Ann. Inst. Henri Poincaré, Analyse Non Linéaire 14,3 (1997), 295-308. | Numdam | MR | Zbl

[6] I. Birindelli - I. Capuzzo Dolcetta - A. Cutri, Indefinite semi-linear equations on the Heisenberg group: a priori bounds and existence, to appear in Comm. Partial Diff. Eq. | MR | Zbl

[7] J.M. Bony, Principe du Maximum, Inégalité de Harnack et unicité du problème de Cauchy pour les operateurs elliptiques dégénérés, Ann. Inst. Fourier Grenobles 19,1 (1969), 277-304. | Numdam | MR | Zbl

[8] G. Citti, Semilinear Dirichlet problem involving critical exponent for the Kohn Laplacian, pre-print.

[9] R.R. Coifman - G. Weiss, Analyse harmonique sur certaines espaces homogènes, in "Lectures Notes in Math.", 242, Springer Verlag, Berlin-Heidelberg-New York, 1971. | MR | Zbl

[10] A. Cutri, "Problemi semilineari ed integro-differenziali per sublaplaciani", PhD Thesis, Università di Roma Tor Vergata, 1997.

[11] V. De Cicco - M.A. Vivaldi, Liouville tipe theorems for weighted elliptic equations, pre-print MeMoMat, Università Roma - La Sapienza, 1997.

[12] G.B. Folland, Fundamental solution for a subelliptic operator, Bull. Amer. Math. Soc. 79 (1973), 373-376. | MR | Zbl

[13] B. Franchi - R.L. Wheeden, Compensation couples and isoperimetric estimates for vector fields, pre-print.

[14] L. Gallardo, Capacités, mouvement brownien et problème de l'épine de Lebesgue sur les groupes de Lie nilpotents, in "Proc. VII Oberwolfach Conference on Probability Measures on Groups", Lectures Notes in Math., 1981. | Zbl

[15] N. Garofalo, book to appear.

[16] N. Garofalo - E. Lanconelli, Existence and non existence results for semilinear equations on the Heisenberg Group, Indiana Univ. Math. Journ. 41 (1992), 71-97. | MR | Zbl

[17] D.S. Jerinson - J.M. Lee, The Yamabe problem on CR manifolds, J. Differential Geometry 25 (1987), 167-197. | MR | Zbl

[18] B. Gaveau, Principe de moindre action, propagation de la chaleur et estimeés sous elliptiques sur certain groupes nilpotents, Acta Math. 139 (1977), 95-153. | MR | Zbl

[19] B. Gidas - J. Spruck, Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math. 35 (1981), 525-598. | MR | Zbl

[20] B. Gidas - J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Diff. Eq. 6, 8 (1981), 883-901. | MR | Zbl

[21] R.W. Goodman, NilpotentLie groups: Structures andApplications toAnalysis, in "Lecture Notes in Math." 562, Berlin-Heidelberg -New York, 1976. | Zbl

[22] G. Hochschild, "The Structure of Lie Groups", Holden-Day Inc., San Francisco, 1965. | MR | Zbl

[23] L. Hormander, Hypoelliptic second order differential equations, Acta Math., Uppsala, 119 (1967), 147-171. | MR | Zbl

[24] M.R. Lancia - M.V. Marchi, Teoremi di Liouville per operatori di tipo fuchsiano sul gruppo di Heisenberg, pre-print, Dipartimento di Matematica, Università di Roma La Sapienza, 1997.

[25] E. Lanconelli - F. Uguzzoni, Asymptotic behaviour and non existence theorems for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg group, pre-print.

[26] D. Neuenschwander, Probabilities on the Heisenberg group, in "Lecture Notes in Math.", 1630, Springer, 1996. | MR | Zbl

[27] O.A. Oleinik - E.V. Radkevic, "Second Order Equations with Nonnegative Characteristic Form", A.M.S. Providence, Plenum Press, 1973. | MR

[28] Y. Pinchover, On positive Liouville's theorems and asymptotic behaviour of solutions of Fuchsian elliptic operators, Ann. Inst. Henri Poincaré, Analyse Non Linéaire 11 (1994) 313-341. | Numdam | MR | Zbl

[29] L.P. Rothschild - E.M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976) 247-320. | MR | Zbl

[30] C.J. Xu, Semilinear subelliptic equations and Sobolev inequality for vector fields satisfying Hörmander condition, Chinese Journal of Contemporary Mathematics 15,2 (1994) 183-192. | MR | Zbl