We prove the strong unique continuation property for manybody 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. Consequently, we obtain the Hohenberg-Kohn theorem for the Maxwell-Schrödinger model.
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. Consequently, we obtain Tellgren's Hohenberg-Kohn theorem for the Maxwell-Schrödinger model.
We consider the homogenization at second-order in ε of Lperiodic Schrödinger operators with rapidly oscillating potentials of the formWe treat both the linear equation with fixed right-hand side and the eigenvalue problem, as well as the case of physical observables such as the integrated density of states. We illustrate numerically that these corrections to the homogenized solution can significantly improve the first-order ones, even when ε is not small.
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