A complete characterization of the existence of extremals for the Trudinger-Moser inequality on ${\mathbb{R}}^2$ under sharp $L^p$-perturbations

Lu Chen, Rou Jiang, Guozhen Lu +1

In this paper, we investigate the following critical Trudinger--Moser inequality on ${\mathbb{R}}^2$ under sharp $L^p$-perturbations: $$ S(λ,p) := \sup_{\substack{u\in H^{1}(\mathbb R…