Exponential integrability in the spirit of Moser-Trudinger's inequalities of functions with finite non-local, non-convex energy

Arka Mallick, Hoai-Minh Nguyen

Let $d\ge 1$, $p\ge d$, and let $\Omega$ be a smooth bounded open subset of ${\mathbb{R}}^d$. We prove some exponential integrability in the spirit of Moser-Trudinger's inequalities for…