An optimal anisotropic Poincaré inequality for convex domains

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 Poincaré 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.

18 pages

References in corpus (3)

• Sharp estimate on the first eigenvalue of the p-Laplacian on compact manifold with nonnegative Ricci curvature
• Bochner-Weitzenboeck formula and Li-Yau estimates on Finsler manifolds
• Sharp Spectral Gap and Li-Yau's Estimate on Alexandrov Spaces

Cited by in corpus (1)

• Anisotropic $p$-capacity and anisotropic Minkowski inequality