An optimal anisotropic Poincar\'e inequality for convex domains
Analysis of PDEs
2017-05-30 v1
Abstract
In this paper, we prove a sharp lower bound of the first (nonzero) eigenvalue of Finsler-Laplacian with the Neumann boundary condition. Equivalently, we prove an optimal anisotropic Poincar\'e inequality for convex domains, which generalizes the result of Payne-Weinberger. A lower bound of the first (nonzero) eigenvalue of Finsler-Laplacian with the Dirichlet boundary condition is also proved.
Keywords
Cite
@article{arxiv.1112.4398,
title = {An optimal anisotropic Poincar\'e inequality for convex domains},
author = {Guofang Wang and Chao Xia},
journal= {arXiv preprint arXiv:1112.4398},
year = {2017}
}
Comments
18 pages