The $L^p$ Dirichlet Problem for the Stokes System on Lipschitz Domains

Joel Kilty

The $L^p$ Dirichlet Problem for the Stokes System on Lipschitz Domains

Analysis of PDEs 2009-05-01 v2

Authors: Joel Kilty

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\"{o}lder condition with exponent $p$ is sufficient for the solvability of the Dirichlet problem with boundary data in $L^p_N(\partial\Omega,\rn{d})$ . Then we obtain a much simpler condition which implies the reverse H\"{o}lder condition. Finally, we establish the solvability ofthe $L^p$ Dirichlet problem for $d\geq 4$ and $2-\varepsilon<p<\frac{2(d-1)}{d-3}+\varepsilon$ .

Keywords

dirichlet problem lp spaces and inequalities operator theory and elliptic operators

Cite

@article{arxiv.0904.3904,
  title  = {The $L^p$ Dirichlet Problem for the Stokes System on Lipschitz Domains},
  author = {Joel Kilty},
  journal= {arXiv preprint arXiv:0904.3904},
  year   = {2009}
}

Comments

To appear in Indiana Univ. Math. Journal. Updated to fix formatting issues

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