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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Semiclassical analysis of general second order elliptic operators on bounded domains
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by E. N. Dancer and J. López-Gómez PDF
Trans. Amer. Math. Soc. 352 (2000), 3723-3742 Request permission

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