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Dispersive estimates and absence of embedded eigenvalues

Herbert Koch, Daniel Tataru (2005)

Journées Équations aux dérivées partielles

In [2] Kenig, Ruiz and Sogge proved u L 2 n n - 2 ( n ) L u L 2 n n + 2 ( n ) provided n 3 , u C 0 ( 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 n + 1 2 and variants thereof.

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