5 papers
Ferronematics: integrality of the limiting interface in the strong coupling regime
Federico Luigi Dipasquale, Yoshihiro Tonegawa
We consider a vectorial energy functional proposed in the physical literature as a simplified model for thin films of ferronematics -- composite materials formed by dispersing magn…
The formation of gradient-driven singular structures of codimension one and two in two-dimensions: The case study of ferronematics. Part~{II}: Refined structure of the energy-concentration set
Giacomo Canevari, Federico Luigi Dipasquale, Bianca Stroffolini
In this paper, we continue our study, started in~\cite{CDS1}, of a two-dimensional variational model for ferronematics -- composite materials formed by dispersing magnetic nanopart…
Liftings of Sobolev maps into closed Riemannian manifolds via double coverings and minimal connections relative to planar sets, with an application to ferronematics
Giacomo Canevari, Federico Luigi Dipasquale, Bianca Stroffolini
We consider Sobolev maps from a planar domain into a closed Riemannian manifold and their BV liftings via a double covering of the target. We establish a sharp lower bound on the j…
The formation of gradient-driven singular structures of codimension one and two in two-dimensions: The case study of ferronematics. Part~I: Energy estimates and compactness results
Giacomo Canevari, Federico Luigi Dipasquale, Bianca Stroffolini
We study a two-dimensional variational model for ferronematics -- composite materials formed by dispersing magnetic nanoparticles into a liquid crystal matrix. The model features t…
Singular extension of critical Sobolev mappings with values into complete Riemannian manifolds
Federico Luigi Dipasquale
Relying on a recent criterion, due to A.~Petrunin [13], to check if a complete, non-compact, Riemannian manifold admits an isometric embedding with positive reach into a Euclidean…