One dimensional symmetry in the Heisenberg group

Isabeau Birindelli; Jyotshana Prajapat

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2001)

  • Volume: 30, Issue: 2, page 269-284
  • ISSN: 0391-173X

How to cite

top

Birindelli, Isabeau, and Prajapat, Jyotshana. "One dimensional symmetry in the Heisenberg group." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 30.2 (2001): 269-284. <http://eudml.org/doc/84442>.

@article{Birindelli2001,
author = {Birindelli, Isabeau, Prajapat, Jyotshana},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {semilinear elliptic equations; Heisenberg Laplacian; one dimensional symmetry; De Giorgi conjecture},
language = {eng},
number = {2},
pages = {269-284},
publisher = {Scuola normale superiore},
title = {One dimensional symmetry in the Heisenberg group},
url = {http://eudml.org/doc/84442},
volume = {30},
year = {2001},
}

TY - JOUR
AU - Birindelli, Isabeau
AU - Prajapat, Jyotshana
TI - One dimensional symmetry in the Heisenberg group
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2001
PB - Scuola normale superiore
VL - 30
IS - 2
SP - 269
EP - 284
LA - eng
KW - semilinear elliptic equations; Heisenberg Laplacian; one dimensional symmetry; De Giorgi conjecture
UR - http://eudml.org/doc/84442
ER -

References

top
  1. [1] L. Ambrosio - X. Cabré, Entire solutions of semilinear elliptic equations in R3 and a conjecture of De Giorgi, J. Amer. Math. Soc.13 (2000), 725-739. Zbl0968.35041MR1775735
  2. [2] M.T. Barlow - R.F. Bass - C. Gui, The Liouville property and a conjecture of De Giorgi, Comm. Pure Appl. Math. 53 (2000), 1007-1038. Zbl1072.35526MR1755949
  3. [3] H. Berestycki - L. Caffarelli - L. Nirenberg, Monotonicity for elliptic equations in unbounded domains, Comm. Pure Appl. Math.50 (1997), 1088-1111. Zbl0906.35035MR1470317
  4. [4] H. Berestycki - F. Hamel - R. Monneau, One-dimensional symmetry of bounded entire solutions of some elliptic equations, Duke Math. J.103 (2000), 375-396. Zbl0954.35056MR1763653
  5. [5] H. Berestycki - L. Nirenberg, On the method of moving planes and the sliding method, Bol. Soc. Bras. Mat.22 (1991), 1-37. Zbl0784.35025MR1159383
  6. [6] H. Berestycki - L. Nirenberg - S.R.S. Varadhan, The principal eigenvalue and maximum principle for second order elliptic operator in general domains, Comm. Pure Appl. Math. (1994), 47-92. Zbl0806.35129MR1258192
  7. [7] I. Birindelli, Hopf's lemma and anti-maximum principle in general domains, J. Differential Equations119 (1995), 450-472. Zbl0831.35114MR1340547
  8. [8] I. Birindelli, Superharmonic functions in the Heisenberg group: estimates and Liouville theorems, to appear in NoDEA. Zbl1290.35127MR1981508
  9. [9] I. Birindelli - J. Prajapat, Nonlinear Liouville theorems in the Heisenberg group via the moving plane method, Comm. Partial Differential Equations24 (1999), 1875-1890. Zbl0944.35023MR1708111
  10. [10] I. Birindelli - J. Prajapat, Monotonicity results for nilpotent stratified groups, Pacific J. Math., to appear. Zbl1158.35305MR1905188
  11. [11] A. Farina, Symmetry for solutions of semilinear elliptic equations in RN and related conjectures, Ricerche di Matematica48 (1999), 129-154. Zbl0940.35084MR1765681
  12. [12] E. De Giorgi, Convergence problems for functionals and operators, Proc. Int. Meeting on Recent Methods in Nonlinear Analysis (Rome1978), Pitagora (ed.), Bologna (1979), pp. 131-188. Zbl0405.49001MR533166
  13. [13] N. Ghoussoub - C. Gui, On a conjecture of De Giorgi and some related problems, Math. Ann.311 (1998), 481-491. Zbl0918.35046MR1637919
  14. [14] D.S. Jerison, Boundary regularity in the Dirichlet problem for □b on CR manifolds, Comm. Pure Appl. Math.36 (1983), 143-181. Zbl0544.35069
  15. [15] D.S. Jerison, The Poincaré inequality for vector fields satisfying Hörmander's condition, Duke Math. J. 53 (1986), 503-523. Zbl0614.35066MR850547
  16. [16] D.S. Jerison, A. Sánchez-Calle, Subelliptic, second order differential operators, Complex analysis, III (College Park, Md., 1985-86), 46-77, Lecture Notes in Math., 1277, Springer, Berlin-New York, 1987. Zbl0634.35017MR922334
  17. [17] Kohn - L. Nirenberg, Non coercive boundary value problems, Comm. Pure Appl. Math.18 (1965), 443-492. Zbl0125.33302MR181815
  18. [18] E.A. Stein, "Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals", Princeton Mathematical Series, 43, 1993. Zbl0821.42001MR1232192
  19. [19] N. Varopoulos - L. Saloff-Coste - T. Coulhon, "Analysis and geometry on groups, Cambridge tracts in Mathematics 100", Cambridge University Press, 1992. Zbl0813.22003MR1218884

NotesEmbed ?

top

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.