4 papers
The Lévy flight foraging hypothesis: comparison between stationary distributions and anomalous diffusion
Serena Dipierro, Giovanni Giacomin, Enrico Valdinoci
We consider a stationary prey in a given region of space and we aim at detecting optimal foraging strategies. On the one hand, when the prey is uniformly distributed, the best poss…
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{|…
Density estimates for a nonlocal variational model with a degenerate double-well potential via the Sobolev inequality
Serena Dipierro, Alberto Farina, Giovanni Giacomin +1
We provide density estimates for level sets of minimizers of the energy $\frac{1}{2} \int_Ω\int_Ω \frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}dxdy+\int_Ω\int_{\mathbb{R}^n\setminusΩ} \frac{|…
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…