The lower bound of first Dirichlet eigenvalue of p-Laplacian in
Riemannian manifolds
The lower bound of first Dirichlet eigenvalue of p-Laplacian in
Riemannian manifolds
This paper investigates the first Dirichlet eigenvalue of bounded domains for the $p$-Laplacian in complete Riemannian manifolds. Firstly, we establish a lower bound for this eigenvalue under the condition that the domain includes a specific function which fulfills certain criteria related to divergence and gradient conditions. As an application, we …