Alessandro Carbotti

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20232026

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math.AP2026

The semigroup generated by linear fractional divergence form operators in $L^{p} (R^{N})$ : the constant coefficient case

Alessandro Carbotti

Let $0 < s < 1$ and $A$ be a constant symmetric positive definite matrix. Given the quadratic form $Q_{A} (u) = \int_{R^{N}} A \nabla^{s} u (x) \cdot \nabla^{s} u (x) d x,$ where $\nabla^{s}$ deno…

math.AP2026

$H$ -convergence and $Γ$ -convergence in the Riesz fractional setting: the nonlinear case

Giuseppe C. Brusca, Maicol Caponi, Alessandro Carbotti +2

This paper concerns the $H$ -convergence of nonlinear nonlocal monotone operators defined through the Riesz fractional gradient and divergence. We show that the $H$ -convergence in t…

math.AP2026

A Brunn-Minkowski inequality for Schrödinger operators with Kato class potentials

Alessandro Carbotti

In this paper we prove a Brunn-Minkowski inequality for the first Dirichlet eigenvalue of a Schrödinger type operator $H_{V} := - div (A \nabla) + V$ , where $V$ is…

math.AP2025

The Polya-Szego principle in the fractional setting: a glimpse on nonlocal functional inequalities

Alessandro Carbotti

In this survey we present the fractional Polya Szego principle and its main consequences in the study of nonlocal functional inequalities. In particular, we show how symmetrization…

math.AP2024

$H$ -compactness for nonlocal linear operators in fractional divergence form

Maicol Caponi, Alessandro Carbotti, Alberto Maione

We study the $H$ -convergence of nonlocal linear operators in fractional divergence form, where the oscillations of the matrices are prescribed outside the reference domain. Our com…

math.AP2023

The viscoelastic paradox in a nonlinear Kelvin-Voigt type model of dynamic fracture

Maicol Caponi, Alessandro Carbotti, Francesco Sapio

In this paper we consider a dynamic model of fracture for viscoelastic materials, in which the constitutive relation, involving the Cauchy stress and the strain tensors, is given i…

The semigroup generated by linear fractional divergence form operators in Lp(RN): the constant coefficient case

H-convergence and Γ-convergence in the Riesz fractional setting: the nonlinear case

A Brunn-Minkowski inequality for Schrödinger operators with Kato class potentials

The Polya-Szego principle in the fractional setting: a glimpse on nonlocal functional inequalities

H-compactness for nonlocal linear operators in fractional divergence form

The viscoelastic paradox in a nonlinear Kelvin-Voigt type model of dynamic fracture

The semigroup generated by linear fractional divergence form operators in $L^{p} (R^{N})$ : the constant coefficient case

$H$ -convergence and $Γ$ -convergence in the Riesz fractional setting: the nonlinear case

$H$ -compactness for nonlocal linear operators in fractional divergence form