A Note on one dimensional symmetry in Carnot groups

Isabeau Birindelli; Ermanno Laconelli

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2002)

  • Volume: 13, Issue: 1, page 17-22
  • ISSN: 1120-6330

Abstract

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In this Note we extend Gibbons conjecture to Carnot groups using the sliding method and the maximum principle in unbounded domains.

How to cite

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Birindelli, Isabeau, and Laconelli, Ermanno. "A Note on one dimensional symmetry in Carnot groups." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 13.1 (2002): 17-22. <http://eudml.org/doc/252353>.

@article{Birindelli2002,
abstract = {In this Note we extend Gibbons conjecture to Carnot groups using the sliding method and the maximum principle in unbounded domains.},
author = {Birindelli, Isabeau, Laconelli, Ermanno},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Monotony properties; Semi-linear equations; Carnot groups; monotony properties; semi-linear equations},
language = {eng},
month = {3},
number = {1},
pages = {17-22},
publisher = {Accademia Nazionale dei Lincei},
title = {A Note on one dimensional symmetry in Carnot groups},
url = {http://eudml.org/doc/252353},
volume = {13},
year = {2002},
}

TY - JOUR
AU - Birindelli, Isabeau
AU - Laconelli, Ermanno
TI - A Note on one dimensional symmetry in Carnot groups
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2002/3//
PB - Accademia Nazionale dei Lincei
VL - 13
IS - 1
SP - 17
EP - 22
AB - In this Note we extend Gibbons conjecture to Carnot groups using the sliding method and the maximum principle in unbounded domains.
LA - eng
KW - Monotony properties; Semi-linear equations; Carnot groups; monotony properties; semi-linear equations
UR - http://eudml.org/doc/252353
ER -

References

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  1. Ambrosio, L. - Cabré, X., Entire solutions of semilinear elliptic equations in R 3 and a conjecture of De Giorgi. J. Amer. Math. Soc., 13, 2000, 725-739. Zbl0968.35041MR1775735DOI10.1090/S0894-0347-00-00345-3
  2. Barlow, M.T. - Bass, R.F. - Gui, C., The Liouville property and a conjecture of De Giorgi. Comm. Pure Appl. Math., 53, 2000, n. 8, 1007-1038. Zbl1072.35526MR1755949DOI10.1002/1097-0312(200008)53:8<1007::AID-CPA3>3.3.CO;2-L
  3. Berestycki, H. - Caffarelli, L. - Nirenberg, L., Monotonicity for Elliptic Equations in Unbounded Domains. Comm. Pure Appl. Math., 50, 1997, 1088-1111. Zbl0906.35035MR1470317DOI10.1002/(SICI)1097-0312(199711)50:11<1089::AID-CPA2>3.0.CO;2-6
  4. Berestycki, H. - Hamel, F. - Monneau, R., One-dimensional symmetry of bounded entire solutions of some elliptic equations. Duke Math. J., 103, 2000, n. 3, 375-396. Zbl0954.35056MR1763653DOI10.1215/S0012-7094-00-10331-6
  5. Berestycki, H. - Nirenberg, L., On the method of moving planes and the sliding method. Bol. Soc. Bras. Mat., vol. 22, 1991, 1-37. Zbl0784.35025MR1159383DOI10.1007/BF01244896
  6. Birindelli, I. - Prajapat, J., One dimensional symmetry in the Heisenberg group. Ann. Scuola Normale Superiore di Pisa, to appear. Zbl1014.35019MR1895712
  7. Bonfiglioli, A. - Lanconelli, E., Maximum Principle on unbounded domains for sub-Laplacians: a Potential Theory approach. Preprint. Zbl1165.35331MR1896411DOI10.1090/S0002-9939-02-06569-3
  8. Farina, A., Symmetry for solutions of semilinear elliptic equations in R N and related conjectures. Ricerche di Matematica, XLVIII, 1999, 129-154. Zbl0940.35084MR1765681
  9. Ghoussoub, N. - Gui, C., On a conjecture of De Giorgi and some related problems. Math. Ann., 311, 1998, 481-491. Zbl0918.35046MR1637919DOI10.1007/s002080050196

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