Non-local, non-convex functionals converging to Sobolev norms

Haim Brezis, Hoai-Minh Nguyen

We study the pointwise convergence and the $\Gamma$-convergence of a family of non-local, non-convex functionals ${\Lambda }_{\delta }$ in $L^p(\Omega )$ for $p>1$. We show that the limits are multiples of $\…