On the Liouville property for fully nonlinear equations

Alessandra Cutrì; Fabiana Leoni

Annales de l'I.H.P. Analyse non linéaire (2000)

  • Volume: 17, Issue: 2, page 219-245
  • ISSN: 0294-1449

How to cite


Cutrì, Alessandra, and Leoni, Fabiana. "On the Liouville property for fully nonlinear equations." Annales de l'I.H.P. Analyse non linéaire 17.2 (2000): 219-245. <http://eudml.org/doc/78492>.

author = {Cutrì, Alessandra, Leoni, Fabiana},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Liouville property},
language = {eng},
number = {2},
pages = {219-245},
publisher = {Gauthier-Villars},
title = {On the Liouville property for fully nonlinear equations},
url = {http://eudml.org/doc/78492},
volume = {17},
year = {2000},

AU - Cutrì, Alessandra
AU - Leoni, Fabiana
TI - On the Liouville property for fully nonlinear equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2000
PB - Gauthier-Villars
VL - 17
IS - 2
SP - 219
EP - 245
LA - eng
KW - Liouville property
UR - http://eudml.org/doc/78492
ER -


  1. [1] Bahri A., Lions P.L., Solutions of superlinear elliptic equations and their Morse indexes, Comm. Pure Appl. Math.45 (1992) 1205-1215. Zbl0801.35026MR1177482
  2. [2] Berestycki H., Capuzzo Dolcetta I., Nirenberg L., Problèmes elliptiques indéfinis et théorèmes de Liouville non-linéaires, C. R. Acad. Sci. Paris, Série I 317 (1993) 945-950. Zbl0820.35056MR1249366
  3. [3] Berestycki H., Capuzzo Dolcetta I., Nirenberg L., Superlinear indefinite elliptic problems and nonlinear Liouville theorems, Topol. Methods Nonlinear Anal.4 (1994) 59-78. Zbl0816.35030MR1321809
  4. [4] Birindelli I., Capuzzo Dolcetta I., Cutrì A., Liouville theorems for semilinear equations on the Heisenberg group, Ann. Inst. Henri Poincaré, Analyse Non Linéaire14 (3) (1997) 295-308. Zbl0876.35033MR1450950
  5. [5] Birindelli I., Capuzzo Dolcetta I., Cutrì A., Indefinite semi-linear equations on the Heisenberg group: a priori bounds and existence, Comm. Partial Differential Equations23 (7-8) (1998) 1123-1157. Zbl0965.35019MR1642599
  6. [6] Birindelli I., Mitidieri E., Liouville theorems for elliptic inequalities and applications, Proc. Royal Soc. Edinburgh128A (1998) 1217-1247. Zbl0919.35023MR1664101
  7. [7] Caffarelli L.A., Interior a priori estimates for solutions of fully nonlinear equations, Ann. Math.130 (1989) 189-213. Zbl0692.35017MR1005611
  8. [8] Caffarelli L.A., Cabré X., Fully Nonlinear Elliptic Equations, American Mathematical Society Colloquium Publications, Vol. 43, AMS, Providence, RI, 1995. Zbl0834.35002MR1351007
  9. [9] Capuzzo Dolcetta I., Teoremi di Liouville e stime a priori per equazioni ellittiche semilineari, Rend. Sem. Mat. Fis. Milano, to appear. 
  10. [10] Capuzzo Dolcetta I., Cutrì A., On the Liouville property for sub-laplacians, Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (4) 25 (1-2) (1997) 239-256. Zbl1042.35013MR1655517
  11. [11] Crandall M.G., Ishii H., Lions P.L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc.27 (1992) 1-67. Zbl0755.35015MR1118699
  12. [12] Cutrì A., Problemi semilineari ed integro-differenziali per sublaplaciani, Ph.D. Thesis, Universitá di Roma Tor Vergata, 1997. 
  13. [13] Gidas B., Spruck J., A priori bounds for positive solutions of nonlinear elliptic equations, Comm. PDE8 (1981) 883-901. Zbl0462.35041MR619749
  14. [14] Gidas B., Spruck J., Global and local behavior of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math.35 (1981) 525-598. Zbl0465.35003MR615628
  15. [15] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer, Berlin, 1983. Zbl0562.35001MR737190
  16. [16] Ishii H., Lions P.L., Viscosity solutions of fully nonlinear second order elliptic partial differential equations, J. Differential Equations83 (1990) 26-78. Zbl0708.35031MR1031377
  17. [17] Hörmander L., Notions of Convexity, Progress in Mathematics, Vol. 127, Birkhäuser, Boston, MA, 1994. Zbl0835.32001MR1301332
  18. [18] Lanconelli E., Uguzzoni F., Asymptotic behaviour and non existence theorems for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg group, Boll. Unione Mat. Ital., Sez B8 (1) (1998). Zbl0902.22006MR1618972
  19. [19] Leoni F., work in preparation. 
  20. [20] Pucci C., Operatori ellittici estremanti, Ann. Mat. Pura Appl.72 (1966) 141-170. Zbl0154.12402MR208150
  21. [21] Protter M.H., Weinberger H.F., Maximum Principles in Differential Equations, Prentice Hall, 1967. Zbl0153.13602MR219861
  22. [22] Ramos M., Terracini S., Troestler C., Problèmes elliptiques surlinéaires avec non-linéarité sans signe défini, C. R. Acad. Sci. Paris, Série I 325 (1997) 283-286. Zbl0884.35042MR1464821
  23. [23] Trudinger N.S., Lectures on nonlinear elliptic equations of second order, in: Lectures in Mathematical Sciences, The University of Tokyo, 1995. 
  24. [24] Uguzzoni F., A Liouville-type theorem on halfspaces for the Kohn laplacian, Proc. Amer. Math. Soc.127 (1) (1999) 117-123. Zbl0907.31006MR1458268
  25. [25] Uguzzoni F., A non existence theorem for a semilinear Dirichlet problem involving critical exponent on halfspaces of the Heisenberg group, NODEA6 (2) (1999). Zbl0961.35054MR1694791

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.