The $L^p$ Dirichlet problem for the Stokes system on Lipschitz domains

Abstract

We study the L P Dirichlet problem for the Stokes system on Lipschitz domains. For any fixed p > 2, we show that a reverse Holder condition with exponent p is sufficient for the solvability of the Dirichlet problem with boundary data in L ρ N (∂Ω, R d ). Then we obtain a much simpler condition which implies the reverse Holder condition. Finally, we establish the solvability of the L p Dirichlet problem for d ≥ 4 and 2 ― e < p < 2(d- 1)/(d-3) +e.