10 papers
Optimal sets for a geometric oscillation energy
Matteo Novaga, Fumihiko Onoue, Emanuele Paolini
We investigate the nonlocal energy corresponding to the -oscillation of the unit normal vector for hypersurfaces, or the unit tangent vector for curves. The energy satisfies geo…
A notion of -fractional mass for -currents in higher codimension
Marco Cicalese, Tim Heilmann, Andrea Kubin +2
In this paper we propose a notion of -fractional mass for -currents in . Such a notion generalizes the notion of -fractional perimeters for sets in the plane to high…
On the shape of hypersurfaces with boundary which have zero fractional mean curvature
Fumihiko Onoue
We consider hypersurfaces with boundary in that are the critical points of the fractional area introduced by Paroni, Podio-Guidugli, and Seguin in [R. Paroni, P. Pod…
On the Shape of Small Liquid Drops Minimizing Nonlocal Energies
Konstantinos Bessas, Matteo Novaga, Fumihiko Onoue
We study the equilibrium shape of liquid drops minimizing the fractional perimeter under the action of a potential energy. We prove, with a quantitative estimate, that the small vo…
Local and Nonlocal Liquid Drop Models
M. Novaga, F. Onoue
We consider some extensions of Gamow's liquid drop model for an atomic nucleus. We present a review of the classical model and then we illustrate some recent developments on a nonl…
Existence of minimizers for a generalized liquid drop model with fractional perimeter
Matteo Novaga, Fumihiko Onoue
We consider the minimization problem of the functional given by the sum of the fractional perimeter and a general Riesz potential, which is one generalization of Gamow's liquid dro…
Local Hölder regularity of minimizers for nonlocal variational problems
Matteo Novaga, Fumihiko Onoue
We study the regularity of solutions to a nonlocal variational problem, which is related to the image denoising model, and we show that, in two dimensions, minimizers have the same…
(Dis)connectedness of nonlocal minimal surfaces in a cylinder and a stickiness property
Serena Dipierro, Fumihiko Onoue, Enrico Valdinoci
We consider nonlocal minimal surfaces in a cylinder with prescribed datum given by the complement of a slab. We show that when the width of the slab is large the minimizers are dis…
Nonexistence of Minimizers for a Nonlocal Perimeter Functional with a Riesz and a Background Potential
Fumihiko Onoue
We consider the nonexistence of minimizers for the energy containing a nonlocal perimeter with a general kernel , a Riesz potential, and a background potential in …
A varifold formulation of mean curvature flow with Dirichlet or dynamic boundary conditions
Yoshikazu Giga, Fumihiko Onoue, Keisuke Takasao
We consider the sharp interface limit of the Allen-Cahn equation with Dirichlet or dynamic boundary conditions and give a varifold characterization of its limit which is formally a…