7 papers
Flat flows of periodic Lipschitz subgraphs for generalized nonlocal perimeters
Lucia De Luca, Antonia Diana, Marcello Ponsiglione
We prove the existence and the 1/2-Hölder continuity in time of flat flows for periodic Lipschitz subgraphs, whose evolution is governed by the gradient flow of generalized nonloca…
Dynamics of screened particles towards equi-spaced ground states
Lucia De Luca, Michael Goldman, Marcello Ponsiglione
This paper deals with the dynamics - driven by the gradient flow of negative fractional seminorms - of empirical measures towards equi-spaced ground states. Specifically, we consid…
A new approach to topological singularities via a weak notion of Jacobian for functions of bounded variation
Lucia De Luca, Riccardo Scala, Nicolas Van Goethem
We introduce a weak notion of -minors of gradients of a suitable subclass of functions. In the case of maps in such a notion extends…
Convergence of supercritical fractional flows to the mean curvature flow
Lucia De Luca, Andrea Kubin, Marcello Ponsiglione
We consider a core-radius approach to nonlocal perimeters governed by isotropic kernels having critical and supercritical exponents, extending the nowadays classical notion of -…
Vectorial crystallization problems and collective behavior
Lucia De Luca, Angelo Ninno, Marcello Ponsiglione
We propose and analyze a class of vectorial crystallization problems, with applications to crystallization of anisotropic molecules and collective behavior such as birds flocking a…
Crystallization to the square lattice for a two-body potential
Laurent Bétermin, Lucia De Luca, Mircea Petrache
We consider two-dimensional zero-temperature systems of particles to which we associate an energy of the form where…
A gradient flow approach to relaxation rates for the multi-dimensional Cahn-Hilliard equation
Michael Goldman, Lucia De Luca, Marta Strani
The aim of this paper is to study relaxation rates for the Cahn-Hilliard equation in dimension larger than one. We follow the approach of Otto and Westdickenberg based on the gradi…