Carleman estimates and necessary conditions for the existence of waveguides Luis EscauriazaLuca FanelliLuis Vega 35B9935J0535J15Carleman estimateswaveguidesunique continuation We study via Carleman estimates the sharpest possible exponential decay for \emph{waveguide} solutions to the Laplace equation \[ (\partial^2_t + \Delta)u = Vu + W\cdot(\partial_t,\nabla)u \] and find a necessary quantitative condition on the exponential decay in the spatial-variable of nonzero waveguide solutions which depends on the size of $V$ and $W$ at infinity. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4710 10.1512/iumj.2012.61.4710 en Indiana Univ. Math. J. 61 (2012) 15 - 30 state-of-the-art mathematics http://iumj.org/access/