582 citations · 1.8k across the 125 of their papers we have counts for
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Splitting theorems, symmetry results and overdetermined problems for Riemannian manifolds
Alberto Farina, Luciano Mari, Enrico Valdinoci
Our work proposes a unified approach to three different topics in a general Riemannian setting: splitting theorems, symmetry results and overdetermined elliptic problems. By the ex…
A fractional framework for perimeters and phase transitions
Enrico Valdinoci
We review some recent results on minimisers of a non-local perimeter functional, in connection with some phase coexistence models whose diffusion term is given by the fractional La…
Some monotonicity results for minimizers in the calculus of variations
Ovidiu Savin, Enrico Valdinoci
We obtain monotonicity properties for minima and stable solutions of general energy functionals of the type under the assumption that a certain inte…
Asymptotics of the -perimeter as
Serena Dipierro, Alessio Figalli, Giampiero Palatucci +1
We deal with the asymptotic behavior of the -perimeter of a set inside a domain as . We prove necessary and sufficient conditions for the existence of such l…
Regularity of nonlocal minimal cones in dimension 2
Ovidiu Savin, Enrico Valdinoci
We show that the only nonlocal -minimal cones in are the trivial ones for all . As a consequence we obtain that the singular set of a nonlocal minimal surfac…
Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian
Serena Dipierro, Giampiero Palatucci, Enrico Valdinoci
This paper deals with the following class of nonlocal Schrödinger equations $$ \displaystyle (-Δ)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1).…