Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem. II: The Pauli Hamiltonian

  • Louis Garrigue

    Ceremade, University Paris-Dauphine, 75016 Paris, France
Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem. II: The Pauli Hamiltonian cover
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Abstract

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

Cite this article

Louis Garrigue, Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem. II: The Pauli Hamiltonian. Doc. Math. 25 (2020), pp. 869–898

DOI 10.4171/DM/765