On the asymptotic behavior for convection-diffusion equations associated to higher order elliptic operators in divergence form

Abstract

We consider the linear convection-diffusion equation associated to higher order elliptic operators (ut + Ltu = aru on Rn × (0,1) u(0) = u0 2 L1(Rn), (1) where a is a constant vector in Rn, m 2 N_, n _ 1 and L0 belongs to a class of higher order elliptic operators in divergence form associated to non-smooth bounded measurable coefficients on Rn. The aim of this paper is to study the asymptotic behavior, in Lp (1 _ p _ 1), of the derivatives Du(t) of the solution of (1) when t tends to 1.