Unique continuation for many-body Schr\"odinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

Unique continuation for many-body Schr\"odinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian

Résumé

We prove the strong unique continuation property for many-body Pauli operators with external potentials, interaction potentials and magnetic fields in $L^p_{\rm loc}(\mathbb{R}^d)$, and with magnetic potentials in $L^q_{\rm loc}(\mathbb{R}^d)$, where $p > \max(2d/3,2)$ and $q > 2d$. For this purpose, we prove a singular Carleman estimate involving fractional Laplacian operators. Consequently, we obtain the Hohenberg-Kohn theorem for the Maxwell-Schr\"odinger model.

Dates et versions

hal-01989476 , version 1 (22-01-2019)

Identifiants

Citer

Louis Garrigue. Unique continuation for many-body Schr\"odinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian. 2019. ⟨hal-01989476⟩
46 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More