107 citations · 369 across the 19 of their papers we have counts for
4 papers · 2 filters
Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: a unified approach via fractional De Giorgi classes
Matteo Cozzi
We study energy functionals obtained by adding a possibly discontinuous potential to an interaction term modeled upon a Gagliardo-type fractional seminorm. We prove that minimizers…
Nonlocal phase transitions in homogeneous and periodic media
Matteo Cozzi, Serena Dipierro, Enrico Valdinoci
We discuss some results related to a phase transition model in which the potential energy induced by a double-well function is balanced by a fractional elastic energy. In particula…
Planelike interfaces in long-range Ising models and connections with nonlocal minimal surfaces
Matteo Cozzi, Serena Dipierro, Enrico Valdinoci
This paper contains three types of results: 1. the construction of ground state solutions for a long-range Ising model whose interfaces stay at a bounded distance from any given hy…
Interior regularity of solutions of non-local equations in Sobolev and Nikol'skii spaces
Matteo Cozzi
We prove interior regularity for weak solutions of linear elliptic integro-differential equations close to the fractional -Laplacian. The result is obtained…