4 papers
Parabolic free boundary phase transition and mean curvature flow
Jingeon An-Lacroix, Kiichi Tashiro
It is known that there is a strong relation between the parabolic Allen--Cahn equation and the mean curvature flow, in the sense that the parabolic Allen--Cahn equation can be cons…
Varifold convergence of free boundary Allen--Cahn equation
Jingeon An-Lacroix, Kiichi Tashiro
The free boundary Allen--Cahn equation in , on has recently attracted considerable attention because it retains th…
Second order estimates for a free boundary phase transition
Jingeon An-Lacroix
It is well known that minimizers of the Allen-Cahn-type functional \[ J_ε(u):=\int_Ω\frac{ε|\nabla u|^2}{2}+\frac{W(u)}ε, \] where is a double-well potential, resemble mini…
Convergence of the fractional Yamabe flow for arbitrary initial energy
Jingeon An-Lacroix, Hardy Chan, Pak Tung Ho
Since the seminal paper of Graham and Zworski (Invent. Math. 2003), conformal geometric problems are studied in the fractional setting. We consider the convergence of fractional Ya…