A Basic Inequality for the Stokes Operator Related to the Navier Boundary Condition
نویسنده
چکیده
We show that ‖Au+∆u‖L2(Ω) ≤ C1‖∇u‖L2(Ω)+C0‖u‖L2(Ω), where u belongs to the domain of A, the Stokes operator for divergence-free vector fields in the domain Ω ⊂ R satisfying the Navier boundary condition. Moreover, in the case of thin domains, the constant C1 is comparable with the small depth of the domains.
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