3 papers
math.AP2025
Density estimates for a (non)local variational model with degenerate double-well potential
Serena Dipierro, Alberto Farina, Giovanni Giacomin +1
In this paper we provide density estimates for a class of functions which includes all the minimizers of the energy $\mathcal{E}_s^p(u,Ω):=(1-s)\left(\frac{1}{2}\int_Ω\int_Ω\frac{|…
math.AP2024
Convex minimizing curves of the scaling-invariant nonlocal Willmore energy
Giovanni Giacomin, Armin Schikorra
We consider the scaling-invariant nonlocal Willmore energy, defined via the nonlocal mean curvature by Caffarelli, Roquejoffre and Savin. Our main result is the existence of minimi…
math.AP2022
Efficiency functionals for the Lévy flight foraging hypothesis
Serena Dipierro, Giovanni Giacomin, Enrico Valdinoci
We consider a forager diffusing via a fractional heat equation and we introduce several efficiency functionals whose optimality is discussed in relation to the Lévy exponent of the…