An optimal anisotropic Poincaré inequality for convex domains

Details An optimal anisotropic Poincaré inequality for convex domains An optimal anisotropic Poincaré inequality for convex domains

2011-12-19

arxiv.org/abs/1112.4398v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

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.

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