Existence and Nonexistence of Extremals for Trudinger-Moser inequalities with $L^p$ type perturbation on any bounded planar domains

Lu Chen, Rou Jiang, Guozhen Lu +1

In this study, we investigate the perturbed Trudinger-Moser inequalities as follows:\[ S_Ω(λ,p)=\sup_{u\in H_{0}^{1}(Ω),\Vert\nabla u\Vert _{L^{2}\left( Ω\right) }\leq 1}\int_Ω\lef…