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arXiv · 1901.03207

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

Louis Garrigue
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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 $L^p\loc(\R^d)$, and with magnetic potentials in ${L^{q}\loc(\R^d)}$, where ${p > \max(2d/3,2)}$ and ${q > 2d}$. For this purpose, we prove a singular Carleman estimate involving fractional Laplacian operators.

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Louis Garrigue. 2019-01-10. Unique continuation for many-body Schr\"odinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian. https://doi.org/10.4171/dm/765

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