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Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian

Garrigue, Louis (2020), Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian, Documenta Mathematica, 25, p. 869–898. 10.4171/DM/765

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Type
Article accepté pour publication ou publié
Date
2020
Journal name
Documenta Mathematica
Volume
25
Published in
Paris
Pages
869–898
Publication identifier
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Author(s)
Garrigue, Louis
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We prove the strong unique continuation property for many-body Pauli operators with external potentials, interaction potentials and magnetic fields in Lploc(Rd), and with magnetic potentials in Lqloc(Rd), 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.
Subjects / Keywords
many-body Pauli operators; magnetic fields; Hohenberg-Kohn theorem; Maxwell-Schrödinger model