5 papers · 1 filter
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…
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…
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…
A strict maximum principle for nonlocal minimal surfaces
Serena Dipierro, Ovidiu Savin, Enrico Valdinoci
In the setting of fractional minimal surfaces, we prove that if two nonlocal minimal sets are one included in the other and share a common boundary point, then they must necessaril…