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math.AP2019★ 1 cited
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★ 4 cited
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…