  Let $\mathbb{F}$ be an algebraically closed field of characteristic $p>3$,
and $\ggg$ the $p$-dimensional Witt algebra over $\mathbb{F}$. Let $\N$ be the
nilpotent cone of $\ggg$. Explicit description of $\N$ is given, so that the
conjugacy classes of Borel subalgebras of $\ggg$ under the automorphism group
are determined. In contrast with only one conjugacy class of Borel subalgebras
in a classical simple Lie algebra, there are two conjugacy classes of Borel
subalgebras in $\ggg$. The representatives of conjugacy classes of Borel
subalgebras, i.e., the so-called standard Borel subalgebras, are precisely
given.
