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math.AP2016★ 4 cited
Global minimizers of the Allen-Cahn equation in dimension
Yong Liu, Kelei Wang, Juncheng Wei
We prove the existence of global minimizers of Allen-Cahn equation in dimensions and above. More precisely, given any strictly area-minimizing Lawson's cones, there are global…
math.AP2016
On Helmholtz equation and Dancer's type entire solutions for nonlinear elliptic equations
Yong Liu, Juncheng Wei
Starting from a bound state (positive or sign-changing) solution to $$ -Δω_m =|ω_m|^{p-1} ω_m -ω_m \ \ \mbox{in}\ \R^n, \ ω_m \in H^2 (\R^n)$$ and solutions to the Helmholtz equati…