A degenerate operator in non divergence form

Abstract

In this paper we consider a fourth order operator in nondivergence form $Au:=a{u}^{\prime \prime \prime \prime }$, where $a:[0,1]\to {\mathcal{R}}_{+}$ 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 $A_{n}u:=a{u}^{(2n)}$.