5 papers · 1 filter
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 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…
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…
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 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 -va…