IUMJ

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

Authors: Joel Kilty

Issue: Volume 58 (2009), Issue 3, 1219-1234

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 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 $2 - \varepsilon<p<2(d - 1)/(d - 3) + \varepsilon$.