Geodesic
Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem. II: The Pauli Hamiltonian
Documenta mathematica, Tome 25 (2020), pp. 869-898
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We prove the strong unique continuation property for many-body Pauli operators with external potentials, interaction potentials and magnetic fields in Llocp​(Rd), and with magnetic potentials in Llocq​(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 Tellgren's Hohenberg-Kohn theorem for the Maxwell-Schrödinger model.
DOI : 10.4171/dm/765
Classification : 26A33, 35J05, 35Q40, 35Q55, 35Q60, 35R11, 81V70, 82M36
Mots-clés : density functional theory, quantum mechanics, unique continuation, many-body theory, Hohenberg-Kohn theorem 
@article{10_4171_dm_765,
     author = {Louis Garrigue},
     title = {Unique {Continuation} for {Many-Body} {Schr\"odinger} {Operators} and the {Hohenberg-Kohn} {Theorem.} {II:} {The} {Pauli} {Hamiltonian}},
     journal = {Documenta mathematica},
     pages = {869--898},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/765},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/765/}
}
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Louis Garrigue. Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem. II: The Pauli Hamiltonian. Documenta mathematica, Tome 25 (2020), pp. 869-898. doi: 10.4171/dm/765

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