Carleman estimates and necessary conditions for the existence of waveguides
Abstract
We study via Carleman estimates the sharpest possible exponential decay for waveguide solutions to the Laplace equation (∂2t+)u=Vu+W·(∂t,∇)u, and find a necessary quantitative condition on the exponential decay in the spatial-variable of nonzero waveguides solutions which depends on the size of V and W at infinity.
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