Article ID Journal Published Year Pages File Type
4609953 Journal of Differential Equations 2015 22 Pages PDF
Abstract

We study the LpLp regularity problem for the stationary Stokes system on Lipschitz domains. For any p>2p>2 we show that a weak reverse Hölder inequality with exponent p   is both necessary and sufficient for the solvability of the regularity problem with data in W1,p(∂Ω)∩Lnp(∂Ω). We also obtain the W1,p(Ω)W1,p(Ω) estimate ‖∇u‖Lp(Ω)+‖q‖Lp(Ω)≤‖f‖Lp(Ω)‖∇u‖Lp(Ω)+‖q‖Lp(Ω)≤‖f‖Lp(Ω) in a bounded Lipschitz domain Ω⊂RdΩ⊂Rd for solutions to the Dirichlet problem Δu=∇q+div(f)Δu=∇q+div(f), div(u)=0div(u)=0 in Ω and u=0u=0 on ∂Ω, where |1p−12|<12d+ε.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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