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The energy method in the Fourier space is useful in deriving the decay estimates for problems in the whole space Rn. In this paper, we study half space problems in R+n=R+×Rn−1 and develop the energy method in the partial Fourier space obtained by taking the Fourier transform with respect to the tangential variable x′∈Rn−1. For the variable x1∈R+ in the normal direction, we use L2 space or weighted...
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