Minimizing the Eigenvalue Ratio for the $p$-Laplacian Operator

Abstract

We focus on the minimization problem of the eigenvalue ratio for the $p$-Laplacian operator with Robin boundary conditions on an interval $[0, \hat{π}],$ where $\hat{\pi} = \frac{2\pi}{p \sin(\pi/p)}.$ Using variational techniques and Prüfer-type transformations, we show that the constant weight is not minimizing for the class of concave weights.