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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On mixed Dirichlet-Neumann eigenvalues of triangles
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by Bartłomiej Siudeja
Proc. Amer. Math. Soc. 144 (2016), 2479-2493
DOI: https://doi.org/10.1090/proc/12888
Published electronically: October 14, 2015

Abstract:

We order the lowest mixed Dirichlet-Neumann eigenvalues of right triangles according to which sides we apply the Dirichlet conditions. It is generally true that the Dirichlet condition on a superset leads to larger eigenvalues, but it is nontrivial to compare e.g. the mixed cases on triangles with just one Dirichlet side. As a corollary we also classify the lowest Neumann and Dirichlet eigenvalues of rhombi according to their symmetry/antisymmetry with respect to the diagonals.

Furthermore, we give an order for the mixed Dirichlet-Neumann eigenvalues on arbitrary triangle, assuming two Dirichlet sides. The single Dirichlet side case is conjectured to also have the appropriate order, following the right triangular case.

References
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Bibliographic Information
  • Bartłomiej Siudeja
  • Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
  • Email: siudeja@uoregon.edu
  • Received by editor(s): February 12, 2015
  • Received by editor(s) in revised form: July 7, 2015
  • Published electronically: October 14, 2015
  • Communicated by: Michael Hitrik
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 2479-2493
  • MSC (2010): Primary 35P15
  • DOI: https://doi.org/10.1090/proc/12888
  • MathSciNet review: 3477064