43 citations · 121 across the 17 of their papers we have counts for
18 papers
Variational principles for the interaction of liquid crystals and electric fields in the Oseen--Frank model
Giovanni Di Fratta, Valeriy Slastikov, Arghir Zarnescu
We develop a rigorous variational framework for uniaxial nematic liquid crystals interacting with an external electric field in the one-constant Oseen--Frank approximation. Equilib…
A Fixed-Point Construction of the Elementary Transcendental Functions
François Alouges, Giovanni Di Fratta, Alberto Fiorenza +1
We present a unified fixed-point construction of the elementary transcendental functions, encompassing the real exponential, the complex exponential (sine and cosine), and the natu…
A Classical Elliptic Regularity Approach to Almost Harmonic Maps and Related Systems
Giovanni Di Fratta
We develop an abstract regularity framework for a class of two-dimensional nonlinear elliptic systems, including almost harmonic maps. The approach combines a Campanato-type iterat…
Reduced theory of symmetric and antisymmetric exchange interactions in nanowires
Giovanni Di Fratta, Filipp N. Rybakov, Valeriy Slastikov
We investigate the behavior of minimizers of perturbed Dirichlet energies supported on a wire generated by a regular simple curve and defined in the space of -val…
A Bourgain-Brezis-Mironescu formula accounting for nonlocal antisymmetric exchange interactions
Elisa Davoli, Giovanni Di Fratta, Rossella Giorgio
The present study concerns the nonlocal-to-local convergence of a family of exchange energy functionals in the limit of very short-range interactions. The analysis accounts for bot…
Korn and Poincaré-Korn inequalities: A different perspective
Giovanni Di Fratta, Francesco Solombrino
We present a concise point of view on the first and the second Korn's inequality for general exponent and for a class of domains that includes Lipschitz domains. Our argument i…
Reduced energies for thin ferromagnetic films with perpendicular anisotropy
G. Di Fratta, C. B. Muratov, V. V. Slastikov
We derive four reduced two-dimensional models that describe, at different spatial scales, the micromagnetics of ultrathin ferromagnetic materials of finite spatial extent featuring…
A modular Poincaré-Wirtinger type inequality on Lipschitz domains for Sobolev spaces with variable exponents
Elisa Davoli, Giovanni Di Fratta, Alberto Fiorenza +1
In the context of Sobolev spaces with variable exponents, Poincaré--Wirtinger inequalities are possible as soon as Luxemburg norms are considered. On the other hand, modular versio…
Sharp conditions for the validity of the Bourgain-Brezis-Mironescu formula
Elisa Davoli, Giovanni Di Fratta, Valerio Pagliari
Following the seminal paper by Bourgain, Brezis and Mironescu, we focus on the asymptotic behavior of some nonlocal functionals that, for each , are defined…
Curved thin-film limits of chiral Dirichlet energies
Giovanni Di Fratta, Valeriy Slastikov
We investigate the curved thin-film limit of a family of perturbed Dirichlet energies in the space of Sobolev maps defined in a tubular neighborhood of an -dimension…
On symmetry of energy minimizing harmonic-type maps on cylindrical surfaces
Giovanni Di Fratta, Alberto Fiorenza, Valeriy Slastikov
The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional in the class of -valued maps defined in cylindrical surfaces. The model nat…
Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation
Giovanni Di Fratta, Carl-Martin Pfeiler, Dirk Praetorius +2
Combining ideas from [Alouges et al. (Numer. Math., 128, 2014)] and [Praetorius et al. (Comput. Math. Appl., 2017)], we propose a numerical algorithm for the integration of the non…
Parking 3-sphere swimmer. I. Energy minimizing strokes
François Alouges, Giovanni Di Fratta
The paper is about the parking 3-sphere swimmer (). This is a low-Reynolds number model swimmer composed of three balls of equal radii. The three balls can move along…
Dimension reduction for the micromagnetic energy functional on curved thin films
Giovanni Di Fratta
Recently a significant interest in ferromagnetic curved thin films has appeared. In particular, thin spherical shells are currently of great interest due to their capability to sup…
Cell averaging two-scale convergence: Applications to periodic homogenization
François Alouges, Giovanni Di Fratta
The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equat…
The Newtonian Potential and the Demagnetizing Factors of the General Ellipsoid
Giovanni Di Fratta
The objective of this paper is to present a modern and concise new derivation for the explicit expression of the interior and exterior Newtonian potential generated by homogeneous…
Homogenization of Composite Ferromagnetic Materials
François Alouges, Giovanni Di Fratta
Nowadays, nonhomogeneous and periodic ferromagnetic materials are the subject of a growing interest. Actually such periodic configurations often combine the attributes of the const…
Half-integer point defects in the -tensor theory of nematic liquid crystals
G. Di Fratta, JM Robbins, V. Slastikov +1
We investigate prototypical profiles of point defects in two dimensional liquid crystals within the framework of Landau-de Gennes theory. Using boundary conditions characteristic o…