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

2009/04/24 by Kilty, Joel
#35Q30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0904.3904

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 Hölder condition with exponent p is sufficient for the solvability of the Dirichlet problem with boundary data in L^p_N(∂Ω,\rnd). Then we obtain a much simpler condition which implies the reverse Hölder condition. Finally, we establish the solvability ofthe L^p Dirichlet problem for d≥ 4 and 2-ε

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