3 papers
math.AP2020
(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…
math.AP2019
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 …
math.AP2018
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…