Breuil's classification of $p$-divisible groups over regular local rings of arbitrary dimension

Let $k$ be a perfect field of characteristic $p\ge 3$. We classify $p$-divisible groups over regular local rings of the form $W(k)[[t_1,\mathrm{.}\mathrm{.}\mathrm{.},t_r,u]]\mathrm{/}(u^e+p{b}_{e-1}{u}^{e-1}+\mathrm{.}\mathrm{.}\mathrm{.}+p{b}_{1}u+p{b}_0)$, where $b_0,\mathrm{.}\mathrm{.}\mathrm{.},b_{e-1}\in W(k)[[t_1,\mathrm{.}\mathrm{.}\mathrm{.},t_r]]$ and $b_0$ is an invertible element. This classification was in the case $r=0$ conjectured by Breuil and proved by Kisin.