49 citations · 69 across the 9 of their papers we have counts for
10 papers
Energy minimization for skyrmions on planar thin films
Giovanni Di Fratta, Michael Innerberger, Dirk Praetorius +1
We consider an energy functional that arises in micromagnetic and liquid crystal theory on thin films. In particular, our energy comprises a non-convex term that models anti-symmet…
Nonlocal Micromagnetics: Compactness Criteria, Existence of Minimizers, and Brown's Fundamental Theorem
Giovanni Di Fratta, Rossella Giorgio, Luca Lombardini
This paper investigates the existence and qualitative properties of minimizers for a class of nonlocal micromagnetic energy functionals defined on bounded domains. The considered e…
Symmetry properties of minimizers of a perturbed Dirichlet energy with a boundary penalization
Giovanni Di Fratta, Antonin Monteil, Valeriy Slastikov
We consider -valued maps on a domain minimizing a perturbation of the Dirichlet energy with vertical penalization in and horizontal penaliz…
Micromagnetics of thin films in the presence of Dzyaloshinskii-Moriya interaction
Elisa Davoli, Giovanni Di Fratta, Dirk Praetorius +1
In this paper, we study the thin-film limit of the micromagnetic energy functional in the presence of bulk Dzyaloshinskii-Moriya interaction (DMI). Our analysis includes both a sta…
Parking 3-sphere swimmer II. The long arm asymptotic regime
François Alouges, Giovanni Di Fratta
The paper carries on our previous investigations on the complementary version of Purcell's rotator: a low-Reynolds-number swimmer composed of three balls of equal radii. In the asy…
Weak-strong uniqueness for the Landau-Lifshitz-Gilbert equation in micromagnetics
Giovanni Di Fratta, Michael Innerberger, Dirk Praetorius
We consider the time-dependent Landau-Lifshitz-Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time.…
Variational principles of micromagnetics revisited
Giovanni Di Fratta, Cyrill B. Muratov, Filipp N. Rybakov +1
We revisit the basic variational formulation of the minimization problem associated with the micromagnetic energy, with an emphasis on the treatment of the stray field contribution…
A short proof of local regularity of distributional solutions of Poisson's equation
Giovanni Di Fratta, Alberto Fiorenza
We prove a local regularity result for distributional solutions of the Poisson's equation with data. We use a very short argument based on Weyl's lemma and Riesz-Fréchet repr…
On a sharp Poincaré-type inequality on the 2-sphere and its application in micromagnetics
Giovanni Di Fratta, Valeriy Slastikov, Arghir Zarnescu
The main aim of this note is to prove a sharp Poincaré-type inequality for vector-valued functions on , that naturally emerges in the context of micromagnetics of sph…
Modular inequalities for the maximal operator in variable Lebesgue spaces
David Cruz-Uribe, Giovanni Di Fratta, Alberto Fiorenza
A now classical result in the theory of variable Lebesgue spaces due to Lerner [A. K. Lerner, On modular inequalities in variable spaces, Archiv der Math. 85 (2005), no. 6, 5…