A regularity result for the bound states of N-body Schrödinger operators: Blow-ups and Lie manifolds
by
Bernd Ammann, Jérémy Mougel, Victor Nistor
A regularity result for the bound states of N-body Schrödinger operators: Blow-ups and Lie manifolds
(.pdf)
Lett. Math. Phys. 113, 26-53 (2023)
Arxiv: https://arxiv.org/abs/2012.13902
DOI: 10.1007/s11005-023-01648-0
©-info: This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this article is published in Journal Mathematical Physics (Springer), and is available online at https://doi.org/10.1007/s11005-023-01648-0
We prove regularity estimates for the eigenfunctions of Schrödinger type operators whose potentials have inverse square singularities and uniform radial limits at infinity. In particular, the usual N-body operators are covered by our result; in that case, the weight is in terms of the (euclidean) distance to the collision planes. The technique of proof is based on blow-ups and Lie manifolds. More precisely, we first blow-up the spheres at infinity of the collision planes to obtain the Georgescu-Vasy compactification and then we blow-up the collision planes. We carefully investigate how the Lie manifold structure and the associated data (metric, Sobolev spaces, differential operators) change with each blow-up. Our method applies also to higher order operators and matrices of scalar operators.
Back to my Homepage
Bernd Ammann
The Paper was written on 28.12.2020
Last update of the webpage 27.02.2023
Impressum und Datenschutzerklärung