A Singular Critical Potential For The Schrodinger operator

2003/10/20 by Thomas Duyckaerts, Duyckaerts, Thomas
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.math/0310309

arxiv created 2003/10/20 · arxiv updated 2009/12/01

Abstract

We construct a potential V on \RR^d, smooth away from one pole, and a sequence of quasi-modes for the operator -Δ+V, which concentrate on this pole. No smoothing effect, Strichartz estimates nor dispersive inequalities hold for the corresponding Schrodinger equation.

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