  In this paper we consider a fourth order operator in nondivergence form $Au:=
au''''$, where $a: [0,1] \rightarrow \mathcal R_+$ is a function that
degenerates somewhere in the interval. We prove that the operator generates an
analytic semigroup, under suitable assumptions on the function $a$. We extend
these results to a general operator $A_nu := au^{(2n)}$.
