29 citations · 39 across the 11 of their papers we have counts for
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math.AP2016★ 1 cited
Approximation of sets of finite fractional perimeter by smooth sets and comparison of local and global -minimal surfaces
Luca Lombardini
In the first part of this paper we show that a set has locally finite -perimeter if and only if it can be approximated in an appropriate sense by smooth open sets. In the se…
math.AP2016★ 29 cited
Complete stickiness of nonlocal minimal surfaces for small values of the fractional parameter
Claudia Bucur, Luca Lombardini, Enrico Valdinoci
In this paper, we consider the asymptotic behavior of the fractional mean curvature when . Moreover, we deal with the behavior of -minimal surfaces when the fractional…
math.AP2016★ 1 cited
Fractional perimeter from a fractal perspective
Luca Lombardini
Following \cite{Visintin}, we exploit the fractional perimeter of a set to give a definition of fractal dimension for its measure theoretic boundary. We calculate the fractal dimen…