Lp resolvent estimates for variable coefficient elliptic systems on Lipschitz domains

Abstract

In this paper, we treat the general strongly elliptic systems with a class of singular potentials on a bounded Lipschitz domain Ω ⊂ ℝd, d ≥ 3. We establish the Lp resolvent estimates on Ω for the above systems with vanishing Dirichlet type or Neumann type boundary value condition, where 2d/(d + 2) - ϵ < p < 2d/(d - 2) + ϵ with some positive constant ϵ = ϵ(Ω).