Subcritical approximation of a Yamabe type non local equation: a Gamma-convergence approach

Abstract

We investigate a natural approximation by subcritical Sobolev embeddings of the Sobolev quotient for the fractional Sobolev spaces $H^s$ for any $0<s<N/2$, using $Γ$-convergence techniques. We show that, for such approximations, optimal functions always exist and exhibit a concentration effect of the $H^s$ energy at one point.