Γ-convergence of concentration problems
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 2 (2003) no. 1, pp. 151-179.

In this paper, we use Γ-convergence techniques to study the following variational problem

S ε F (Ω):=supε -2 * Ω F(u)dx: Ω |u| 2 dxε 2 ,u=0 on Ω,
where 0F(t)|t| 2 * , with 2 * =2n n-2, and Ω is a bounded domain of n , n3. We obtain a Γ-convergence result, on which one can easily read the usual concentration phenomena arising in critical growth problems. We extend the result to a non-homogeneous version of problem S ε F (Ω). Finally, a second order expansion in Γ-convergence permits to identify the concentration points of the maximizing sequences, also in some non-homogeneous case.

Classification: 35J60, 35C20, 49J45
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Amar, Micol; Garroni, Adriana. $\Gamma $-convergence of concentration problems. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 2 (2003) no. 1, pp. 151-179. http://archive.numdam.org/item/ASNSP_2003_5_2_1_151_0/

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