The $L^p$ Dirichlet problem for the Stokes system on Lipschitz domains Joel Kilty 35Q30Stokes systemLipschitz domainsDirichlet problem We study the $L^p$ Dirichlet problem for the Stokes system on Lipschitz domains. For any fixed $p>2$, we show that a reverse H\"older condition with exponent $p$ is sufficient for the solvability of the Dirichlet problem with boundary data in $L^p_N(\partial\Omega,\mathbb{R}^{d})$. Then we obtain a much simpler condition which implies the reverse H\"older condition. Finally, we establish the solvability of the $L^p$ Dirichlet problem for $d\geq4$ and $2 - \varepsilon<p<2(d - 1)/(d - 3) + \varepsilon$. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3568 10.1512/iumj.2009.58.3568 en Indiana Univ. Math. J. 58 (2009) 1219 - 1234 state-of-the-art mathematics http://iumj.org/access/