5 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…
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…