Calculus of Variations and Geometric Measure Theory

G. Palatucci - A. Pisante - Y. Sire

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

created by palatucci on 28 Jun 2013
modified on 18 Dec 2015


Published Paper

Inserted: 28 jun 2013
Last Updated: 18 dec 2015

Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5)
Volume: 14
Number: 3
Pages: 819-840
Year: 2015
Doi: 10.2422/2036-2145.201302_006


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 $\Gamma$-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.

Keywords: Nonlocal variational problems, critical Sobolev exponent, Concentration-compactness principle, fractional Sobolev spaces