3 papers
math.AP2020
Prescribed mean curvature equation on torus
Yuki Tsukamoto
Prescribed mean curvature problems on the torus has been considered in one dimension. In this paper, we prove the existence of a graph on the -dimensional torus ,…
math.AP2019
The Dirichlet problem for a prescribed mean curvature equation
Yuki Tsukamoto
We study a prescribed mean curvature problem where we seek a surface whose mean curvature vector coincides with the normal component of a given vector field. We prove that the prob…
math.AP2019
A diffused interface with the advection term in a Sobolev space
Yoshihiro Tonegawa, Yuki Tsukamoto
We study the asymptotic limit of diffused surface energy in the van der Waals--Cahn--Hillard theory when an advection term is added and the energy is uniformly bounded. We prove th…