Liouville theorems for semilinear equations on the Heisenberg group

I. Birindelli; I. Capuzzo Dolcetta; A. Cutrì

Annales de l'I.H.P. Analyse non linéaire (1997)

  • Volume: 14, Issue: 3, page 295-308
  • ISSN: 0294-1449

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Birindelli, I., Capuzzo Dolcetta, I., and Cutrì, A.. "Liouville theorems for semilinear equations on the Heisenberg group." Annales de l'I.H.P. Analyse non linéaire 14.3 (1997): 295-308. <http://eudml.org/doc/78412>.

@article{Birindelli1997,
author = {Birindelli, I., Capuzzo Dolcetta, I., Cutrì, A.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Heisenberg Laplacian},
language = {eng},
number = {3},
pages = {295-308},
publisher = {Gauthier-Villars},
title = {Liouville theorems for semilinear equations on the Heisenberg group},
url = {http://eudml.org/doc/78412},
volume = {14},
year = {1997},
}

TY - JOUR
AU - Birindelli, I.
AU - Capuzzo Dolcetta, I.
AU - Cutrì, A.
TI - Liouville theorems for semilinear equations on the Heisenberg group
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1997
PB - Gauthier-Villars
VL - 14
IS - 3
SP - 295
EP - 308
LA - eng
KW - Heisenberg Laplacian
UR - http://eudml.org/doc/78412
ER -

References

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  1. [1] H. Berestycki, I. Capuzzo Dolcetta and L. Nirenberg, Problèmes elliptiques indéfinis et théorèmes de Liouville non-linéaires, C. R. Acad. Sci. Paris , Série I, Vol. 317, 1993, pp. 945-950. Zbl0820.35056MR1249366
  2. [2] H. Berestycki, I. Capuzzo Dolcetta and L. Nirenberg, Superlinear indefinite elliptic problems and nonlinear Liouville theorems. Topological Methods in Nonlinear Analysis, Vol. 4.1, 1995, pp. 59-78. Zbl0816.35030MR1321809
  3. [3] I. Birindelli, I. Capuzzo Dolcetta and A. Cutri, Indefinite semi-linear equations on the Heisenberg group: a priori bounds and existence, Preprint. Zbl0876.35033MR1642599
  4. [4] J.M. Bony, Principe du Maximum, Inégalité de Harnack et unicité du problème de Cauchy pour les operateurs elliptiques dégénérés, Ann. Inst. Fourier Grenobles, Vol. 19,1,1969, pp. 277-304. Zbl0176.09703MR262881
  5. [5] M. Esteban and P.-L. Lions, Existence and non-existence results for semilinear elliptic problems in unbounded domainsProc. R.S.E.(A), Vol. 93A,1982, pp. 1-14. Zbl0506.35035MR688279
  6. [6] G.B. Folland, Fondamental solution for subelliptic operators, Bull. Amer. Math. Soc., Vol. 79, 1979, pp. 373-376. Zbl0256.35020MR315267
  7. [7] G.B. Folland and E.M. Stein, Estimates for the ∂h complex and analysis on the Heisenberg Group, Comm. Pure Appl.Math., Vol. 27, 1974, pp. 492-522. Zbl0293.35012MR367477
  8. [8] N. Garofalo and E. Lanconelli, Existence and non existence results for semilinear equations on the Heisenberg group, Indiana Univ. Math. Journ., Vol. 41, 1992, pp. 71-97. Zbl0793.35037MR1160903
  9. [9] B. Gaveau, Principe de moindre action, propagation de la chaleur et estimeé sous elliptiques sur certain groups nilpotents, Acta Math., Vol. 139, 1977, pp. 95-153. Zbl0366.22010MR461589
  10. [10] B. Gidas and J. SpruckGlobal and local behavior of positive solutions of nonlinear elliptic equationsComm. Pure Appl. Math, Vol. 35, 1981, pp. 525-598. Zbl0465.35003MR615628
  11. [11] D. Gilbarg and N.S. TrudingerElliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. Zbl0562.35001MR737190
  12. [12] P.C. Greiner, Spherical harmonics in the Heisenberg group, Canad. Math. Bull., Vol. 23 (4), 1980, pp. 383-396. Zbl0496.22012MR602590
  13. [13] L. Hormander, Hypoelliptic second order differential equations, Acta Math., Uppsala, Vol. 119, 1967, pp. 147-171. Zbl0156.10701MR222474

Citations in EuDML Documents

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  1. Francesco Uguzzoni, Asymptotic behavior of solutions of Schrödinger inequalities on unbounded domains of nilpotent Lie groups
  2. Alessandra Cutrì, Fabiana Leoni, On the Liouville property for fully nonlinear equations
  3. Italo Capuzzo Dolcetta, Alessandra Cutrì, On the Liouville property for sublaplacians
  4. Alessandra Cutrì, Problemi semilineari ed integro-differenziali per Sublaplaciani
  5. E. Lanconelli, F. Uguzzoni, Asymptotic behavior and non-existence theorems for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg group

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