Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds
Grant Keady, Benchawan Wiwatanapataphee · Mathematical Inequalities & Applications · 2018
Amongst N -dimenstional 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 various related inequalities which are amenable to investigation using the formulae for the eigenvalues.