From the 1 of 35 linked papers with an AI index.
35 papers
On the minimal diameter of finite covers
Yifei Cai, Qiliang Luo
We prove that every closed hyperbolic surface admits a sequence of finite covers with asymptotically optimal diameters.
A logistic equation with non-local operators of order near zero
Luigi Appolloni, Serena Dipierro, Enrico Valdinoci
In this paper we study an equation driven by a non-local operator of order "near zero" with mixed Dirichlet-Neumann boundary conditions, modelling a biological system consisting of…
A free boundary problem driven by boundary distance in the coincidence set
Amal Alphonse, Enrico Valdinoci, Marcelo Bongarti
We study a free boundary problem of minimising a functional containing a non-local term rewarding depth into the zero phase: for on a bounded, open set $Ω\subset\ma…
Homoclinic solutions for nonlocal equations and applications to the theory of atom dislocation
Serena Dipierro, Caterina Sportelli, Enrico Valdinoci
The paper proves the existence of homoclinic solutions for fractional Laplacian equations with gradient-type forcing and shows how these solutions describe crystal configurations i…
Nonlocal minimal surfaces are generically unique, and smooth in one extra dimension
Serena Dipierro, Xavier Fernández-Real, Enrico Valdinoci
We study the fractional Plateau problem for -minimal sets with prescribed exterior datum. For fixed exterior data, minimizers need not be unique, and singularities may occur bey…
A free boundary analysis of tumor invasion driven by angiogenesis
Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli +1
We discuss a free boundary model for tumor invasion that describes a cloud of cells that diffuse and, at the same time, are drifted along the vector field of the chemotactic direct…