On the Moser-Trudinger inequality in fractional Sobolev-Slobodeckij spaces

Enea Parini, Bernhard Ruf

We consider the problem of finding the optimal exponent in the Moser-Trudinger inequality \[ \sup \left\{\int_Ω\exp{\left(α\,|u|^{\frac{N}{N-s}}\right)}\,\bigg|\,u \in \widetilde{W…