A semi-linear problem for the Heisenberg laplacian

Isabeau Birindelli; Alessandra Cutrì

Rendiconti del Seminario Matematico della Università di Padova (1995)

  • Volume: 94, page 137-153
  • ISSN: 0041-8994

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Birindelli, Isabeau, and Cutrì, Alessandra. "A semi-linear problem for the Heisenberg laplacian." Rendiconti del Seminario Matematico della Università di Padova 94 (1995): 137-153. <http://eudml.org/doc/108366>.

@article{Birindelli1995,
author = {Birindelli, Isabeau, Cutrì, Alessandra},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Dirichlet problem; sub-elliptic operator; existence of positive solutions; principal eigenvalue; Hopf type lemma; embedding theorem},
language = {eng},
pages = {137-153},
publisher = {Seminario Matematico of the University of Padua},
title = {A semi-linear problem for the Heisenberg laplacian},
url = {http://eudml.org/doc/108366},
volume = {94},
year = {1995},
}

TY - JOUR
AU - Birindelli, Isabeau
AU - Cutrì, Alessandra
TI - A semi-linear problem for the Heisenberg laplacian
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1995
PB - Seminario Matematico of the University of Padua
VL - 94
SP - 137
EP - 153
LA - eng
KW - Dirichlet problem; sub-elliptic operator; existence of positive solutions; principal eigenvalue; Hopf type lemma; embedding theorem
UR - http://eudml.org/doc/108366
ER -

References

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  1. [1] H. Amann - M.G. Crandall, On some existence theorems for semilinear elliptic equations, Indiana Univ. Math. Journ., 27, 5 (1978), pp. 779-790. Zbl0391.35030MR503713
  2. [2] J.M. Bony, Principe du Maximum, Inégalité de Harnack et unicité du problème de Cauchy pour les operateurs elliptiques dégénérés, Ann. Inst. Fourier Grenobles, 19, 1 (1969), pp. 277-304. Zbl0176.09703MR262881
  3. [3] H. Berestycki - I. Capuzzo Dolcetta - L. Nirenberg, Problèmes Elliptiques indéfinis et Théorème de Liouville non-linéaires, C. R. Acad. Sci. Paris, Série I, 317 (1993), pp. 945-950. Zbl0820.35056MR1249366
  4. [4] G.B. Folland, Subelliptic estimates and function spaces on nilpotent Lie group, Ark. Mat., 13 (1975), pp. 161-220. Zbl0312.35026MR494315
  5. [5] G.B. Folland, Fondamental solution for subelliptic operators, Bull. Amer. Math. Soc., 79, (1979), pp. 373-376. Zbl0256.35020MR315267
  6. [6] G.B. Folland - E.M. Stein, Estimates for the ∂h complex and analysis on the Heisenberg Group, Comm. Pure Apll. Math., 27 (1974), pp. 492-522. Zbl0293.35012
  7. [7] N. Garofalo - E. LANCONELLI, Existence and non existence results for semilinear Equations on the Heisenberg Group, Indiana Univ. Math. Journ., 41 (1992), pp. 71-97. Zbl0793.35037MR1160903
  8. [8] B. Gidas - W. M. NI - L. NIRENBERG, Symmetry and related Properties via the Maximum Principle, Commun. Math. Phys., 68 (1979), pp. 209-243. Zbl0425.35020MR544879
  9. [9] L. Hormander, Hypoelliptic second order differential equations, Acta Math., Uppsala, 119 (1967), pp. 147-171. Zbl0156.10701MR222474
  10. [10] D.S. Jerison, The Dirichlet Problem for the Kohn Laplacian on the Heisenberg group, II, J. Funct. Anal., 43 (1981), pp. 224-257. Zbl0493.58022MR633978
  11. [11] D. Jerison - A. Sànchez-Calle, Subelliptic second order differential operator, Lecture Notes in Math., 1277, Berlin-Heidelberg-New York (1987), pp. 46-77. Zbl0634.35017MR922334
  12. [12] J. Serrin, A symmetry problem in potential theory, Arch. Ration. Mech., 43 (1971), pp. 304-318. Zbl0222.31007MR333220

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