Bounds to the first eigenvalues of weighted p-Steklov and (p,q)-Laplacian Steklov problems

TL;DR

This paper establishes upper bounds for the first eigenvalues of weighted p-Laplacian and (p,q)-Laplacian Steklov problems on submanifolds, extending classical spectral estimates to weighted and nonlinear settings.

Contribution

It provides new Reilly-type upper bounds for the first eigenvalues of weighted p-Laplacian and (p,q)-Laplacian Steklov problems on submanifolds with boundary.

Findings

Derived upper bounds for first eigenvalues

Extended classical estimates to weighted nonlinear operators

Applicable to submanifolds in Euclidean spaces

Abstract

We consider the Steklov problem associated with the weighted p-Laplace operator and $(p,q)$-Laplacian on submanifolds with the boundary of Euclidean spaces and prove Reilly-type upper bounds for their first eigenvalues.