Maximal Lp-Lq regularity for the Stokes equations with various boundary conditions in the half space
Abstract
We prove resolvent Lp estimates and maximal Lp-Lq regularity estimates for the Stokes equations with Dirichlet, Neumann and Robin boundary conditions in the half space. Each solution is constructed by a Fourier multiplier of x'-direction and an integral of xN-direction. We decompose the solution such that the symbols of the Fourier multipliers are bounded and holomorphic. We see that the operator norms are dominated by a homogeneous function of order -1 for xN-direction. The basis are Weis's operator-valued Fourier multiplier theorem and a boundedness of a kernel operator. We give a new simple approach to get maximal regularity in the half space.
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