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Journées équations aux dérivées partielles

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Herbert Koch; Daniel Tataru
Dispersive estimates and absence of embedded eigenvalues
Journées équations aux dérivées partielles (2005), Exp. No. 6, 10 p., doi: 10.5802/jedp.19
Article PDF | Analyses MR 2352775

Résumé - Abstract

In [2] Kenig, Ruiz and Sogge proved

$$ \Vert u \Vert _{L^{\frac{2n}{n-2}}(\mathbb{R}^n)} \lesssim \Vert L u \Vert _{L^{\frac{2n}{n+2}}(\mathbb{R}^n)} $$

provided $n \ge 3$, $u \in C^{\infty }_0(\mathbb{R}^n)$ and $L$ is a second order operator with constant coefficients such that the second order coefficients are real and nonsingular. As a consequence of [3] we state local versions of this inequality for operators with $C^2$ coefficients. In this paper we show how to apply these local versions to the absence of embedded eigenvalues for potentials in $L^{\frac{n+1}{2}}$ and variants thereof.


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