We study via Carleman estimates the sharpest possible exponential decay for waveguide solutions to the Laplace equation (partial derivative(2)(t) + Delta)u = Vu + W . (partial derivative(t), del)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.
Carleman estimates and necessary conditions for the existence of waveguides / L., Escauriaza; Fanelli, Luca. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - STAMPA. - 61:1(2012), pp. 15-30. [10.1512/iumj.2012.61.4710]
Carleman estimates and necessary conditions for the existence of waveguides
FANELLI, Luca
2012
Abstract
We study via Carleman estimates the sharpest possible exponential decay for waveguide solutions to the Laplace equation (partial derivative(2)(t) + Delta)u = Vu + W . (partial derivative(t), del)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.File allegati a questo prodotto
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