7 papers
Nonlocal eigenvalue problems and superposition operators
Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli +1
We study the spectral theory of mixed local and nonlocal operators with lower-order terms in the right-hand side of the equation. This kind of problems is motivated by the analysis…
Nonlocal approximation of minimal surfaces: optimal estimates from stability
Hardy Chan, Serena Dipierro, Joaquim Serra +1
Minimal surfaces in closed 3-manifolds are classically constructed via the Almgren-Pitts approach. The Allen-Cahn approximation has proved to be a powerful alternative, and Chodosh…
Elliptic partial differential equations from an elementary viewpoint
Serena Dipierro, Enrico Valdinoci
These notes are the outcome of some courses taught to undergraduate and graduate students from the University of Western Australia, the Pontif\'ıcia Universidade Católica do Rio…
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…
Some nonlocal formulas inspired by an identity of James Simon
Serena Dipierro, Jack Thompson, Enrico Valdinoci
Inspired by a classical identity proved by James Simons, we establish a new geometric formula in a nonlocal, possibly fractional, setting. Our formula also recovers the classical c…
A Brezis-Nirenberg type result for mixed local and nonlocal operators
Stefano Biagi, Serena Dipierro, Enrico Valdinoci +1
We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. In particular, we investigate the corresponding…