A Paneitz-Branson type equation with Neumann boundary conditions
Analysis of PDEs
2019-10-11 v2
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 non-constant 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.
Keywords
Cite
@article{arxiv.1903.10275,
title = {A Paneitz-Branson type equation with Neumann boundary conditions},
author = {Denis Bonheure and Hussein Cheikh Ali and Robson Nascimento},
journal= {arXiv preprint arXiv:1903.10275},
year = {2019}
}
Comments
23 pages. To appear in Adv. Cal. Var