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On the growth of nonlocal catenoids
Matteo Cozzi, Enrico Valdinoci
As well known, classical catenoids in possess logarithmic growth at infinity. In this note we prove that the case of nonlocal minimal surfaces is significantly dif…
Bernstein-Moser-type results for nonlocal minimal graphs
Matteo Cozzi, Alberto Farina, Luca Lombardini
We prove a flatness result for entire nonlocal minimal graphs having some partial derivatives bounded from either above or below. This result generalizes fractional versions of cla…
Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic media
Matteo Cozzi, Enrico Valdinoci
We consider here a nonlocal phase transition energy in a periodic medium and we construct solutions whose interfaces lie at a bounded distance from any given hyperplane. These solu…
Fractional De Giorgi classes and applications to nonlocal regularity theory
Matteo Cozzi
We present some recent results obtained by the author on the regularity of solutions to nonlocal variational problems. In particular, we review the notion of fractional De Giorgi c…