Low Frequency Estimates for Long Range Perturbations in Divergence Form

Bouclet, Jean-Marc

Canadian journal of mathematics, Tome 63 (2011) no. 5, pp. 961-991

Résumé

We prove a uniformcontrol as $z\,\to \,0$ for the resolvent ${{(P-z)}^{-1}}$ of long range perturbations $P$ of the Euclidean Laplacian in divergence form by combining positive commutator estimates and properties of Riesz transforms. These estimates hold in dimension $d\,\ge \,3$ when $P$ is defined on ${{\mathbb{R}}^{d}}$ and in dimension $d\,\ge \,2$ when $P$ is defined outside a compact obstacle with Dirichlet boundary conditions.

Détail

DOI : 10.4153/CJM-2011-022-9

Mots-clés : 35P25, resolvent estimates, thresholds, scattering theory, Riesz transform

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