Geodesic
Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds
Shubin, Mikhail1 
1 Department of Mathematics, Northeastern University, Boston, MA 02115, USA
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 15, 22 p.

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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.

Classification : 35P05, 58G25, 47B25, 81Q10

Shubin, Mikhail 1

1 Department of Mathematics, Northeastern University, Boston, MA 02115, USA 
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     title = {Essential self-adjointness for magnetic {Schr\"odinger} operators on non-compact manifolds},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
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     pages = {1--22},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {1998-1999},
     zbl = {1061.58021},
     mrnumber = {1721333},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEDP_1998-1999____A15_0/}
}
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Shubin, Mikhail. Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1998-1999), Exposé no. 15, 22 p.. http://geodesic.mathdoc.fr/item/SEDP_1998-1999____A15_0/