5 citations · 9 across the 6 of their papers we have counts for
7 papers
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…
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 operators in divergence form and existence theory for integrable data
David Arcoya, Serena Dipierro, Edoardo Proietti Lippi +2
We present an existence and uniqueness result for weak solutions of Dirichlet boundary value problems governed by a nonlocal operator in divergence form and in the presence of a da…
Optimal embedding results for fractional Sobolev spaces
Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli +1
This paper deals with the fractional Sobolev spaces , with and . Here, we use the interpolation results in [4] to provide suitable condi…
Global perturbative elliptic problems with critical growth in the fractional setting
Serena Dipierro, Edoardo Proietti Lippi, Enrico Valdinoci
Given , , and a bounded and integrable function which is strictly positive in an open set, we show that there exist at least two nonnegative solutions of the…
The Neumann condition for the superposition of fractional Laplacians
Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli +1
We present a new functional setting for Neumann conditions related to the superposition of (possibly infinitely many) fractional Laplace operators. We will introduce some bespoke f…
(Non)local logistic equations with Neumann conditions
Serena Dipierro, Edoardo Proietti Lippi, Enrico Valdinoci
We consider here a problem of population dynamics modeled on a logistic equation with both classical and nonlocal diffusion, possibly in combination with a pollination term. The en…