A sharp Trudinger-Moser inequality on any bounded and convex planar domain

Guozhen Lu, Qiaohua Yang

Wang and Ye conjectured in [22]: Let $\Omega$ be a regular, bounded and convex domain in ${\mathbb{R}}^2$. There exists a finite constant $C(\Omega )>0$ such that \[ \int_Ωe^{\frac{4πu^{2}}{H…