# Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds

Mikhail Shubin^{[1]}

- [1] Department of Mathematics, Northeastern University, Boston, MA 02115, USA

Séminaire Équations aux dérivées partielles (1998-1999)

- Volume: 1998-1999, page 1-22

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topShubin, Mikhail. "Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds." Séminaire Équations aux dérivées partielles 1998-1999 (1998-1999): 1-22. <http://eudml.org/doc/10965>.

@article{Shubin1998-1999,

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.},

affiliation = {Department of Mathematics, Northeastern University, Boston, MA 02115, USA},

author = {Shubin, Mikhail},

journal = {Séminaire Équations aux dérivées partielles},

language = {eng},

pages = {1-22},

publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},

title = {Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds},

url = {http://eudml.org/doc/10965},

volume = {1998-1999},

year = {1998-1999},

}

TY - JOUR

AU - Shubin, Mikhail

TI - Essential self-adjointness for magnetic Schrödinger operators on non-compact manifolds

JO - Séminaire Équations aux dérivées partielles

PY - 1998-1999

PB - Centre de mathématiques Laurent Schwartz, École polytechnique

VL - 1998-1999

SP - 1

EP - 22

AB - 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.

LA - eng

UR - http://eudml.org/doc/10965

ER -

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