9 citations · 35 across the 70 of their papers we have counts for
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Enhanced boundary regularity of planar nonlocal minimal graphs, and a butterfly effect
Serena Dipierro, Aleksandr Dzhugan, Nicolò Forcillo +1
In this note, we showcase some recent results concerning the stickiness properties of nonlocal minimal graphs in the plane. To start with, the nonlocal minimal graphs in the plane…
Boundary properties of fractional objects: flexibility of linear equations and rigidity of minimal graphs
Serena Dipierro, Ovidiu Savin, Enrico Valdinoci
The main goal of this article is to understand the trace properties of nonlocal minimal graphs in~, i.e. nonlocal minimal surfaces with a graphical structure. We establish th…
On divergent fractional Laplace equations
Serena Dipierro, Ovidiu Savin, Enrico Valdinoci
We consider the divergent fractional Laplace operator presented in [Dipierro-Savin-Valdinoci, Rev. Mat. Iberoam.] and we prove three types of results. Firstly, we show that any giv…
Singularity formation in fractional Burgers' equations
Giuseppe Maria Coclite, Serena Dipierro, Francesco Maddalena +1
The formation of singularities in finite time in non-local Burgers' equations, with time-fractional derivative, is studied in detail. The occurrence of finite time singularity is p…
Alessio Figalli's contributions to nonlocal minimal surfaces
Serena Dipierro, Enrico Valdinoci
Alessio has produced in his very intense career an extraordinary number of outstanding results in an impressive variety of topics. Among the multifold research lines in which he ac…
Nonlocal minimal graphs in the plane are generically sticky
Serena Dipierro, Ovidiu Savin, Enrico Valdinoci
We prove that nonlocal minimal graphs in the plane exhibit generically stickiness effects and boundary discontinuities. More precisely, we show that if a nonlocal minimal graph in…