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arXiv · 1909.02160

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

Haim Brezis·Hoai-Minh Nguyen
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Abstract

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 $\int_{\Omega} |\nabla u|^p$. This is a continuation of our previous work where the case $p=1$ was considered.

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Haim Brezis, Hoai-Minh Nguyen. 2019-09-05. Non-local, non-convex functionals converging to Sobolev norms. https://arxiv.org/abs/1909.02160

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