Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2018

Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem

Résumé

We prove the strong unique continuation property for many-body Schrödinger operators with an external potential and an interaction potential both in $L^p_{\rm{loc}}(\mathbb{R}^d)$, where p > 2 if d = 3 and p = max(2d/3, 2) otherwise, independently of the number of particles. With the same assumptions , we obtain the Hohenberg-Kohn theorem, which is one of the most fundamental results in Density Functional Theory.
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Dates et versions

hal-01770288 , version 1 (20-04-2018)
hal-01770288 , version 2 (21-05-2018)
hal-01770288 , version 3 (29-05-2018)
hal-01770288 , version 4 (01-03-2019)

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Louis Garrigue. Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem. 2018. ⟨hal-01770288v1⟩
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