Fourth-order differential operators with interior degeneracy and generalized Wentzell boundary conditions

Abstract

In this article we consider the fourth-order operators \(A_1u:=(au'')''\) and \(A_2u:=au''''\) in divergence and non divergence form, where \(a:[0,1]\to\mathbb{R}_+\) degenerates in an interior point of the interval. Using the semigroup technique, under suitable assumptions on \(a\), we study the generation property of these operators associated to generalized Wentzell boundary conditions. We prove the well posedness of the corresponding parabolic problems.