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
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10.1512/iumj.2009.58.3568
10.1512/iumj.2009.58.3568
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Indiana Univ. Math. J. 58 (2009) 1219 - 1234
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