Evolution equations on non flat waveguides

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D'ANCONA, Piero, Reinhard RACKE, 2010. Evolution equations on non flat waveguides

@techreport{DAncona2010Evolu-630, series={Konstanzer Schriften in Mathematik}, title={Evolution equations on non flat waveguides}, year={2010}, number={273}, author={D'Ancona, Piero and Racke, Reinhard} }

2011-03-22T17:45:17Z D'Ancona, Piero 2010 We investigate the dispersive properties of evolution equations on waveguides with a non flat shape. More precisely we consider an operator<br />H=-Delta_{x}-Delta_{y}+V(x,y)<br />with Dirichled boundary condition on an unbounded domain Omega, and we introduce the notion of a repulsive waveguide along the direction of the first group of variables x. If Omega is a repulsive waveguide, we prove a sharp estimate for the Helmholtz equation Hu-lambda u=f. As consequences we prove smoothing estimates for the Schrödinger and wave equations associated to H, and Strichartz estimates for the Schrödinger equation. Additionally, we deduce that the operator H does not admit eigenvalues. Racke, Reinhard Racke, Reinhard application/pdf Evolution equations on non flat waveguides 2011-03-22T17:45:17Z D'Ancona, Piero eng terms-of-use

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