par Bonheure, Denis ;Cheikh-Ali, Hussein ;Nascimento, Robson
Référence Advances in Calculus of Variations, page (1--21), ahead of print
Publication Publié, 2019-08-11
Article révisé par les pairs
Résumé : We consider the best constant in a critical Sobolev inequality of second order. We show non-rigidity for the optimizers above a certain threshold, namely, we prove that the best constant is achieved by a nonconstant solution of the associated fourth order elliptic problem under Neumann boundary conditions. Our arguments rely on asymptotic estimates of the Rayleigh quotient. We also show rigidity below another threshold.