*Published Paper*

**Inserted:** 17 feb 2011

**Last Updated:** 23 dec 2011

**Journal:** Rend. Sem. Mat. Univ. Padova

**Volume:** 125

**Pages:** 1-14

**Year:** 2011

**Links:**
http://rendiconti.math.unipd.it/volumes/downloads_closed/RSMUP_2011__125__1_0.pdf

**Abstract:**

Let $\Omega$ be a general, possibly non-smooth, bounded domain of $\mathbb{R}^N$, $N\geq 3$. Let $\displaystyle 2^{*}\!\!=\!{2N}\,\!/{(N-2)}$ be the critical Sobolev exponent. We study the following variational problem
$$
S^{{}}** _{{\varepsilon}=\sup\left} \{ \int_{{\Omega}u}^{{2}^{{}**}\!-\varepsilon}dx: \int

**Keywords:**
G-convergence, concentration, critical exponent, Sobolev inequality

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