Semiclassical analysis of general second order elliptic operators on bounded domains
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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.References
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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
- Received by editor(s): August 13, 1997
- Received by editor(s) in revised form: April 21, 1998
- Published electronically: March 21, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 3723-3742
- MSC (2000): Primary 35P15, 35J10, 35B25
- DOI: https://doi.org/10.1090/S0002-9947-00-02534-4
- MathSciNet review: 1694285