Denis Bonheure, Hussein Cheikh Ali, Robson Nascimento
Published 2019-03-25Version 1
We consider the best constant in a critical Sobolev inequality of second order. We show non-rigidity for the optimizers above a certain treshold, 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 treshold.
Lyapunov inequalities for Neumann boundary conditions at higher eigenvalues
Fractional diffusion with Neumann boundary conditions: the logistic equation
Ergodic problems and periodic homogenization for fully nonlinear equations in half-space type domains with Neumann boundary conditions
![QR code for arXiv:1903.10275 [math.AP]](http://oss.arxitics.com/images/favicon.svg)