5 papers
-convergence and -convergence in the Riesz fractional setting: the nonlinear case
Giuseppe C. Brusca, Maicol Caponi, Alessandro Carbotti +2
This paper concerns the -convergence of nonlinear nonlocal monotone operators defined through the Riesz fractional gradient and divergence. We show that the -convergence in t…
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 , where is…
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…
-compactness for nonlocal linear operators in fractional divergence form
Maicol Caponi, Alessandro Carbotti, Alberto Maione
We study the -convergence of nonlocal linear operators in fractional divergence form, where the oscillations of the matrices are prescribed outside the reference domain. Our com…
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…