One dimensional symmetry in the Heisenberg group

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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

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