Formula omitted] resolvent estimates for constant coefficient elliptic systems on Lipschitz domains

Abstract

In this paper, we establish the Lp resolvent estimates on a Lipschitz domain Ω in Rd for constant coefficient elliptic systems with homogeneous Neumann boundary conditions, where 1<p<∞ for d=3, and 2d/(d+3)−ϵ<p<2d/(d−3)+ϵ for d≥4 with some positive constant ϵ=ϵ(Ω). We also give the global Lp estimates for the derivatives of solutions to the previous systems, where 2≤p<2d/(d−1)+ϵ for d≥3. Finally we extend our main results to the case of some variable coefficient elliptic systems on a bounded Lipschitz domain.