A non-existence theorem for a semilinear Dirichlet problem involving critical exponent on halfspaces of the Heisenberg group

Let Delta(n)(II) be the Kohn Laplacian on the Heisenberg group H-n and let Q = 2n + 2 be the homogeneous dimension of H-n. In this note, completing a recent result obtained with E. Lanconelli [ 9], we prove that, if Pi is a halfspace of H-n, then the critical Dirichlet problem (*) - Delta H-n u = u Q+2/uQ-2 in Pi, u = 0 in partial derivative Pi has no nontrivial nonnegative weak solutions. This result enables to improve a representation theorem by Citti [ 2], for Palais-Smale sequences related to the equation in (*).