The compactness and the concentration compactness via $p$-capacity

T. V. Anoop, Ujjal Das

For $p\in (1,N)$ and $\Omega \subseteq {\mathbb{R}}^N$ open, the Beppo-Levi space ${\mathcal{D}}_0^{1,p}(\Omega )$ is the completion of $C_c^{\infty }(\Omega )$ with respect to the norm $\left( \int_Ω|\…