22 citations · 102 across the 16 of their papers we have counts for
16 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…
Fractional Sobolev spaces via interpolation, and applications to mixed local-nonlocal operators
Alberto Maione
In this note, we present a well-known connection between the Sobolev-Slobodeckij spaces, also known as Fractional Sobolev spaces, and interpolation theory. We show how Sobolev spac…
Variational convergences under moving anisotropies
Alberto Maione, Fabio Paronetto, Simone Verzellesi
We study the asymptotic behaviour of sequences of integral functionals depending on moving anisotropies. We introduce and describe the relevant functional setting, establishing uni…
-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…
Schrödinger-Maxwell equations driven by mixed local-nonlocal operators
Nicolò Cangiotti, Maicol Caponi, Alberto Maione +1
In this paper we prove existence of solutions to Schrödinger-Maxwell type systems involving mixed local-nonlocal operators. Two different models are considered: classical Schröding…
Klein-Gordon-Maxwell equations driven by mixed local-nonlocal operators
Nicolò Cangiotti, Maicol Caponi, Alberto Maione +1
Classical results concerning Klein-Gordon-Maxwell type systems are shortly reviewed and generalized to the setting of mixed local-nonlocal operators, where the nonlocal one is allo…
Phase field model for multi-material shape optimization of inextensible rods
Patrick Dondl, Alberto Maione, Steve Wolff-Vorbeck
We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization pr…
Variational methods for nonpositive mixed local-nonlocal operators
Alberto Maione, Dimitri Mugnai, Eugenio Vecchi
We prove the existence of a weak solution for boundary value problems driven by a mixed local--nonlocal operator. The main novelty is that such an operator is allowed to be nonposi…
-convergence of elliptic and parabolic operators depending on vector fields
Alberto Maione, Fabio Paronetto, Eugenio Vecchi
We consider sequences of elliptic and parabolic operators in divergence form and depending on a family of vector fields. We show compactness results with respect to G-convergence,…
-convergence for functionals depending on vector fields. II. Convergence of minimizers
Alberto Maione, Andrea Pinamonti, Francesco Serra Cassano
Given a family of locally Lipschitz vector fields on , , we study integral functionals depending on . Using the results in \c…
Maz'ya-Shaposhnikova formula in Magnetic Fractional Orlicz-Sobolev spaces
Alberto Maione, Ariel Martin Salort, Eugenio Vecchi
In this note we prove the validity of the Maz'ya-Shaposhnikova formula in magnetic fractional Orlicz-Sobolev spaces. This complements a previous study of the limit as $s \uparrow 1…
On the Maz'ya-Shaposhnikova formula in Orlicz-Sobolev spaces on Carnot groups
Marco Capolli, Alberto Maione, Ariel Martin Salort +1
In this note we study the limit as of fractional Orlicz-Sobolev seminorms in Carnot groups. This closes the study started in [10]
Integral representation of local left--invariant functionals in Carnot groups
Alberto Maione, Eugenio Vecchi
The aim of this note is to prove a representation theorem for left--invariant functionals in Carnot groups. As a direct consequence, we can also provide a -convergence result fo…
Asymptotic behaviours in Fractional Orlicz-Sobolev spaces on Carnot groups
Marco Capolli, Alberto Maione, Ariel Martin Salort +1
In this article we define a class of fractional Orlicz-Sobolev spaces on Carnot groups and, in the spirit of the celebrated results of Bourgain-Brezis-Mironescu and of Maz'ya-Shapo…
-convergence for equations depending on monotone operators in Carnot groups
Alberto Maione
Let be an open and bounded subset of a Carnot Group and . In this paper we present some results related to the convergence of solutions of Dirichle…
-convergence for functionals depending on vector fields. I. Integral representation and compactness
Alberto Maione, Andrea Pinamonti, Francesco Serra Cassano
Given a family of locally Lipschitz vector fields on , , we study functionals depending on . We prove an integral representat…