Carleman estimates and necessary conditions for the existence of waveguides

Details Carleman estimates and necessary conditions for the existence of waveguides Carleman estimates and necessary conditions for the existence of waveguides

2011-05-16

arxiv.org/abs/1105.3230v1

Mathematics

Analysis of PDEs

12 pages

Scientific paper

We study via Carleman estimates the sharpest possible exponential decay for {\it waveguide} solutions to the Laplace equation $$(\partial^2_t+\triangle)u=Vu+W\cdot(\partial_t,\nabla)u,$$ 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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