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math.AP2025
Maz'ya-type bounds for sharp constants in fractional Poincaré-Sobolev inequalities
Francesco Bozzola, Matteo Talluri
We prove estimates for the sharp constants in fractional Poincaré-Sobolev inequalities associated to an open set, in terms of a nonlocal capacitary extension of its inradius. This…
math.AP2025
On a fractional semilinear Neumann problem arising in Chemotaxis
Eleonora Cinti, Matteo Talluri
We study a semilinear and nonlocal Neumann problem, which is the fractional analogue of the problem considered by Lin--Ni--Takagi in the '80s. The model under consideration arises…
math.AP2025
Barycentric stability of nonlocal perimeters: the convex case
Chiara Gambicchia, Enzo Maria Merlino, Berardo Ruffini +1
In this work, we establish a sharp form of a nonlocal quantitative isoperimetric inequality involving the barycentric asymmetry for convex sets. This result can be seen as the nonl…