par Bonheure, Denis ;Cheikh-Ali, Hussein ;Alves Do Nascimento Filho, Robson
Référence Advances in Calculus of Variations, 14, 4, page (499-519)
Publication Publié, 2021-10-01
Article révisé par les pairs
Résumé : Abstract 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.