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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Semiclassical analysis of general second order elliptic operators on bounded domains


Authors: E. N. Dancer and J. López-Gómez
Journal: Trans. Amer. Math. Soc. 352 (2000), 3723-3742
MSC (2000): Primary 35P15, 35J10, 35B25
Published electronically: March 21, 2000
MathSciNet review: 1694285
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Abstract:

In this work we ascertain the semiclassical behavior of the fundamental energy and the ground state of an arbitrary second order elliptic operator, not necessarily selfadjoint, on a bounded domain. Our analysis provides us with substantial improvements of many previous results found in the context of quantum mechanics for $C^\infty$ perturbations of the Laplacian.


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Additional Information

E. N. Dancer
Affiliation: Department of Mathematics, The University of Sydney, Sydney, N.S.W. 2006, Australia
Email: normd@maths.usyd.edu.au

J. López-Gómez
Affiliation: Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040-Madrid, Spain
Email: julian@sunma4.mat.ucm.es

DOI: https://doi.org/10.1090/S0002-9947-00-02534-4
Received by editor(s): August 13, 1997
Received by editor(s) in revised form: April 21, 1998
Published electronically: March 21, 2000
Article copyright: © Copyright 2000 American Mathematical Society