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Séminaire Équations aux dérivées partielles (Polytechnique)

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Mikhail Shubin
Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds
Séminaire Équations aux dérivées partielles (Polytechnique) (1998-1999), Exp. No. 15, 22 p.
Article PDF | Analyses MR 1721333 | Zbl 1061.58021 | 1 citation dans Cedram
Class. Math.: 35P05, 58G25, 47B25, 81Q10

Résumé - Abstract

We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [29,30,31], a shorter and more transparent proof of which was provided by the author in [41]. The main idea, as in [41], consists in an explicit use of the Lipschitz analysis on the Riemannian manifold and also by additional geometrization arguments which include a use of a metric which is conformal to the original one with a factor depending on the minorant of the electric potential.

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