For the Fourier modes of the linearized inner problem, the solution size is at most a constant times 1/ω times the weighted forcing size, and this 1/ω growth is optimal.
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On a linear equation arising in the study of phase separation of Bose-Einstein condensates
For the Fourier modes of the linearized inner problem, the solution size is at most a constant times 1/ω times the weighted forcing size, and this 1/ω growth is optimal.