Degenerate fourth order parabolic equations with Neumann boundary conditions

Abstract

We study the generation property for a fourth order operator in divergence or in non divergence form with suitable Neumann boundary conditions. As a consequence we obtain the well posedness for the parabolic equations governed by these operators. The novelty of this paper is that the operators depend on a function $a:[0,1]\to {\mathbb{R}}_{+}$ that degenerates somewhere in the interval.