Entire monotone solutions of the anisotropic Allen-Cahn equation in dimension 5

In this paper, we consider the anisotropic Allen-Cahn equation $-\operatorname{div} a(Du)+W'(u)=0$ in $\mathbb{R}^N$, where $a(p):=DH(p)$ with $H(p)=\frac{1}{2}F(p)^2$ and $F$ a uniformly elliptic integrand, and $W(u)=\frac{1}{4}(1-u^2)^2$. Based on the Mooney-Yang anisotropic minimal graph, we prov