8 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…
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…