TY - JOUR
T1 - Dirichlet eigenvalue sums on triangles are minimal for equilaterals
AU - Laugesen, Richard Snyder
AU - Siudeja, Bartłomiej Andrzej
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2011/12
Y1 - 2011/12
N2 - Among all triangles of given diameter, the equilateral triangle is shown to minimize the sum of the first n eigenvalues of the Dirichlet Laplacian, for each n ≥ 1. In addition, the first, second and third eigenvalues are each proved to be minimal for the equilateral triangle. The disk is conjectured to be the minimizer among general domains.
AB - Among all triangles of given diameter, the equilateral triangle is shown to minimize the sum of the first n eigenvalues of the Dirichlet Laplacian, for each n ≥ 1. In addition, the first, second and third eigenvalues are each proved to be minimal for the equilateral triangle. The disk is conjectured to be the minimizer among general domains.
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U2 - 10.4310/cag.2011.v19.n5.a2
DO - 10.4310/cag.2011.v19.n5.a2
M3 - Article
AN - SCOPUS:84857331109
VL - 19
SP - 855
EP - 885
JO - Communications in Analysis and Geometry
JF - Communications in Analysis and Geometry
SN - 1019-8385
IS - 5
ER -