22 citations · 102 across the 20 of their papers we have counts for
21 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…
Maximum principles and spectral analysis for the superposition of operators of fractional order
Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli +1
We consider a "superposition operator" obtained through the continuous superposition of operators of mixed fractional order, modulated by a signed Borel finite measure defined over…
Logistic diffusion equations governed by the superposition of operators of mixed fractional order
Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli +1
We discuss the existence of stationary solutions for logistic diffusion equations of Fisher-Kolmogoroff-Petrovski-Piskunov type driven by the superposition of fractional operators…
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…