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Matteo Talluri

Publications and source records attributed to Matteo Talluri.

5 recordsLinked to original sources
arXiv2026

Existence and non-existence results for a fractional Lane-Emden equation with nonlocal Neumann conditions

We consider the fractional Lane-Emden equation with a nonlocal Neumann condition in a half-space. We establish the existence of non-constant solutions for the critical problem in any dimension. On the other hand, we show that, in dimension $n=1$, the subcritical problem admits only the trivial solution. This result follows from a new Pohozaev-type identity, which we obtain by using suitable decay estimates for the solutions.

math.AP↗
arXiv2025

Maz'ya-type bounds for sharp constants in fractional Poincar\'e-Sobolev inequalities

We prove estimates for the sharp constants in fractional Poincar\'e-Sobolev inequalities associated to an open set, in terms of a nonlocal capacitary extension of its inradius. This work builds upon previous results obtained in the local case by Maz'ya and Shubin and by the first author and Brasco. We rely on a new Maz'ya-Poincar\'e inequality and, incidentally, we also prove new fractional Poincar\'e-Wirtinger-type estimates. These inequalities display sharp limiting behaviours with respect to the fractional order of differentiability. As a byproduct, we obtain a new criterion for the embedding of the homogeneous Sobolev space $\mathcal{D}^{s,p}_0(\Omega)$ in $L^q(\Omega)$, valid in the subcritical regime and for $p \le q < p^*_s$. Our results are new even for the first eigenvalue of the fractional Laplacian and contain an optimal characterization for the positivity of the fractional Cheeger's constant.

math.AP↗
arXiv2025

On a fractional semilinear Neumann problem arising in Chemotaxis

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 in the description of stationary configurations of the Keller--Segel model for chemotaxis, when a nonlocal diffusion for the concentration of the chemical is considered. In particular, we extend to any fractional power $s\in (0,1)$ of the Laplacian (with homogeneous Neumann boundary conditions) the results obtained in [20] for $s=1/2$. We prove existence and some qualitative properties of non--constant solutions when the diffusion parameter $\varepsilon$ is small enough, and on the other hand, we show that for $\varepsilon$ large enough any solution must be necessarily constant.

math.AP↗