Estimates on the first eigenvalues of q-Wentzell-Laplace problem

Abstract

In this study‎, ‎we consider the first eigenvalues associated with the $q$-Wentzell-Laplace problem on a compact submanifold $\mathcal{M}$ that possesses a boundary $\partial \mathcal{M}$ and we obtain Reilly-type upper bounds for these eigenvalues‎. ‎Our findings‎, ‎in particular scenarios‎, ‎align with the results presented in \cite{Ro4}‎. ‎Additionally‎, ‎we investigate the upper bounds of these eigenvalues within the context of product manifolds $\mathbb{R}\times \mathcal{M}$‎.