Existence and non-existence of maximizers for the Moser-Trudinger type inequalities under inhomogeneous constraints

Norihisa Ikoma, Michinori Ishiwata, Hidemitsu Wadade

In this paper, we study the existence and non-existence of maximizers for the Moser-Trudinger type inequalities in ${\mathbb{R}}^N$ of the form \[ D_{N,α}(a,b):= \sup_{u\in W^{1,N}(\Bbb…