Carleman estimates and necessary conditions for the existence of waveguides

Luis Escauriaza; Luca Fanelli; Luis Vega

Carleman estimates and necessary conditions for the existence of waveguides

Analysis of PDEs 2011-05-18 v1

Authors: Luis Escauriaza , Luca Fanelli , Luis Vega

Abstract

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.

Keywords

Carleman estimates waveguide solutions Laplace equation exponential decay partial differential equations

Cite

@article{arxiv.1105.3230,
  title  = {Carleman estimates and necessary conditions for the existence of waveguides},
  author = {Luis Escauriaza and Luca Fanelli and Luis Vega},
  journal= {arXiv preprint arXiv:1105.3230},
  year   = {2011}
}

Comments

12 pages

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