Quantitative flatness results and $BV$-estimates for stable nonlocal minimal surfaces
Quantitative flatness results and $BV$-estimates for stable nonlocal minimal surfaces
We establish quantitative properties of minimizers and stable sets for nonlocal interaction functionals, including the $s$-fractional perimeter as a particular case. On the one hand, we establish universal $BV$-estimates in every dimension $n \geqslant 2$ for stable sets. Namely, we prove that any stable set in $B_1$ has finite classical …