Isoperimetric inequalities for eigenvalues of triangles
Bartlomiej Siudeja
35P15eigenvaluessymmetrizationpolarizationvariational methodspolynomial inequalities
Isoperimetric lower bounds for the first eigenvalue for the Dirichlet Laplacian on arbitrary triangles are proved using various symmetrization techniques. It is also shown that among triangles, the equilateral triangle maximizes the spectral gap and (under additional assumption) the ratio of the first two eigenvalues.
Indiana University Mathematics Journal
2010
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10.1512/iumj.2010.59.3744
10.1512/iumj.2010.59.3744
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Indiana Univ. Math. J. 59 (2010) 1097 - 1120
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