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D. Jerison, John Lee (1987)
The Yamabe problem on CR manifoldsJournal of Differential Geometry, 25
G. Talenti (1976)
Best constant in Sobolev inequalityAnnali di Matematica Pura ed Applicata, 110
M. Esteban, P. Lions (1982)
Existence and non-existence results for semilinear elliptic problems in unbounded domainsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 93
A. Bahri, J. Coron (1988)
On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domainCommunications on Pure and Applied Mathematics, 41
G. Citti (1995)
Semilinear Dirichlet problem involving critical exponent for the Kohn LaplacianAnnali di Matematica Pura ed Applicata, 169
E. Lanconelli, Francesco Uguzzoni (1998)
Asymptotic behavior and non-existence theorems for semilinear Dirichlet problems involving critical exponent on unbounded domains of the Heisenberg groupBollettino Della Unione Matematica Italiana
P. L. Lions (1985)
The concentration-compactness principle in the calculus of variations. The limit caseRev. Mat. Iberoamericana, 1
H. Brezis (1983)
437Comm. Pure Appl. Math., 36
Paris Vz
Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents Haim Brezis
Francesco Uguzzoni (1999)
A non-existence theorem for a semilinear Dirichlet problem involving critical exponent on halfspaces of the Heisenberg groupNonlinear Differential Equations and Applications NoDEA, 6
G. Folland (1973)
A fundamental solution for a subelliptic operatorBulletin of the American Mathematical Society, 79
V. Benci, G. Cerami (1990)
Existence of positive solutions of the equation −Δu + a(x)u = u(N + 2)(N − 2) in RNJournal of Functional Analysis, 88
N. Garofalo, E. Lanconelli (1992)
Existence and nonexistence results for semilinear equations on the Heisenberg groupIndiana University Mathematics Journal, 41
Ann. Univ. Ferrara - Sez. VII - Sc. Mat. Suppl. Vol. XLV, 187-195 (1999) E. LANCONELLI (*) To the memory of Lamberto Cattabriga 1. - Introduction. In this note we report on a series of results by G. Citti, F. Uguzzoni and the present author concerning the Dirichlet boundary value problem for semilin- ear equation with critical behavior on the Heisenberg group. We begin by recalling some definitions and some basic known results. The Heisenberg group H ~, whose points will be denoted by ~ = (z, t) = (x, y, t), is the Lie group (R 2~ +1, o) with composition law defined by ~..,~' = (z +z', t +t' +2((x', y)- (x, y'))) where (,} denotes the inner product in R" . As is well known, the linear second order partial differential operator j=l where (1) Xj=~xj+2yj~t, Yj=3yj-2xj~t, je{1, ..., n}, is called the Kohn Laplacian on H'. The operator A H" has nonnegative defined characteristic form with mini- mum eigenvalue identically zero. Then A Hn is degenerate elliptic and not ellip- tic at any point. However, due to a well known theorem of HSrmander, the Kohn Laplacian is a sub-elliptic hypoelliptic operator since the Lie algebra
ANNALI DELL UNIVERSITA DI FERRARA – Springer Journals
Published: Jan 1, 1999
Keywords: Critical Exponent; Heisenberg Group; Nonnegative Solution; Nonlinear Elliptic Equation; Yamabe Problem
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