Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds
Abstract
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.
Citation
Keady, G. and Wiwatanapataphee, B. 2018. Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds. Mathematical Inequalities and Applications. 21 (4): pp. 911-930.
Source Title
Mathematical Inequalities and Applications
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School
School of Electrical Engineering, Computing and Mathematical Science (EECMS)
Remarks
Copyright 2018 Ele-Math. Reproduced with permission.
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