Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds
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Copyright 2018 Ele-Math. Reproduced with permission.
Amongst N-dimensional rectangular parallelepipeds (boxes) of a given volume, that which has the smallest fundamental Robin eigenvalue for the Laplacian is the N -cube. We give an elementary proof of this isoperimetric inequality based on the well-known formulae for the eigenvalues. Also treated are variously related inequalities which are amenable to investigation using the formulae for the eigenvalues.
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