On the Liouvìlle Property for Sublaplacians

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Volumn 25, Issue 1-2, 1997, Pages 239-256

  Dolcetta, Italo Capuzzo ^a   Cutrì, Alessandra ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009247546     PISSN: 0391173X     EISSN: 20362145     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. H . B E R E S T Y C K I - I . CAPUZZO DOLCETTA - L . NIRENBERG, Problèmes elliptiques indéfinis et théorèmes de Liouville non-linéaires, C. R. Acad. Sci. Paris, Série 1 3 1 7 (1993), 945-950.
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.
3. S. BiAGiNi, Positive solutions for a semilinear equation on the Heisenberg group. Bull. U M I 9, B (1995), 883-900.
4. I . BiRiNDELLi, Nonlinear Liouville theorems, to appear in "Reaction Diffusion Systems", Caristi and Mitidieri (eds)
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.
6. I . B I R I N D E L L I - I . C A P U Z Z O D O L C E T T A - A . C U T R I, Indefinite semi-linear equations on the Heisenberg group: a priori bounds and existence, to appear in Comm. Partial Diff. E q .
7. J . M . BONY, Principe du Maximum, Inégalité de Hamack et unicité du problème de Cauchy pour les operateurs elliptiques dégénérés, Ann. Inst. Fourier Grenobles 1 9, 1 (1969), 277¬ 304.
8. G . O T T I, 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.", 2 4 2, Springer Veriag, BerUn-Heidelberg-New York, 1971.
10. A. CUTRI, "Problemi semihneari ed integro-differenziaU per sublaplaciani", PhD Thesis, Università di Roma Tor Vergata, 1997.
11. V. D E QCCO - M . A . VIVALDI, Liouville tipe theorems for weighted elliptic equations, pre-print MeMoMat, Università Roma - La Sapienza, 1997.
12. G. B. FOLLANO, Fundamental solutionfor a subelliptic operator, Bull. Amer. Math. Soc. 79 (1973), 373-376.
13. B . F R A N C H I - R . L . W H E E D E N, Compensation couples and isoperimetric estimates for vector fields, pre-print.
14. L . G A L L A R D O, Capacités, mouvement brownien et problème de Vépine de Lebesgue sur les groupes de Lie nilpotents, in "Proc. V I I Oberwolfach Conference on Probability Measures on Groups", Lectures Notes in Math., 1981.
15. N. GAROFALO, book to appear.
16. N. GAROFALO - E . LANCONELLI, Existence and non existence resultsfor semilinear equations on the Heisenberg Group, Indiana Univ. Math. Joum. 41 (1992), 71-97.
17. D. S. JERINSON - J . M . LEE, The Yamabeproblem on CR manifolds, J . Difiercntiai Geometry 25 (1987), 167-197.
18. B. CAVEAU, Principe de moindre action, propagation de la chaleur et estimées sous elliptiques sur certain groupes nilpotents. Acta Math. 1 3 9 (1977), 95-153.
19. B. GiDAS - J. SPRUCK, Global and local behavior ofpositive solutions ofnonlinearelliptic equations. Comm. Pure Appi. Math. 35 (1981), 525-598.
20. B. CiDAS - J. SPRUCK, A priori boundsforpositive solutions ofnonlinearelliptic equations. Comm. Partial Diff. Eq. 6, 8 (1981), 883-901.
21. R . W. GOODMAN, NilpotentLie groups: Structures andApplications toAnalysis, in "Lecture Notes in Math." 5 6 2, Berlin-Heidelberg-New York, 1976.
22. G. HOCHSCHILD, "The Structure of Lie Groups", Holden-Day Inc., San Francisco, 1965.
23. L . HORM ANDER, Hypoelliptic second order differential equations. Acta Math., Uppsala, 1 1 9 (1967), 147-171.
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.
27. O. A. OLEINIK - E . V. RADKEVIC, "Second Order Equations with Nonnegative Characteristic Form", A.M.S. Providence, Plenum Press, 1973.
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.
29. L . P. ROTHSCHILD - E . M . STEm, Hypoelliptic differential operators and nilpotent groups. Acta Math. 137 (1976) 247-320.
30. C. J. X U, Semilinear subelliptic equations and Sobolev inequality for vectorfields satisfying Hörmander condition, Chinese Journal of Contemporary Mathematics 1 5, 2 (1994) 183-192.