Isocapacitary constants associated with $p$-Laplacian on graphs

TL;DR

This paper introduces isocapacitary constants for the $p$-Laplacian on graphs and uses them to estimate the first eigenvalues of various boundary value problems, advancing spectral graph theory.

Contribution

It defines isocapacitary constants for the $p$-Laplacian on graphs and applies these to derive eigenvalue estimates for different $p$-Laplacian problems.

Findings

Derived estimates for first eigenvalues of Dirichlet, Neumann, and Steklov $p$-Laplacian problems

Established a connection between isocapacitary constants and spectral properties on graphs

Extended spectral analysis techniques to nonlinear $p$-Laplacian operators

Abstract

In this paper, we introduce isocapacitary constants for the $p$-Laplacian on graphs and apply them to derive estimates for the first eigenvalues of the Dirichlet $p$-Laplacian, the Neumann $p$-Laplacian, and the $p$-Steklov problem.