An optimal anisotropic Poincaré inequality for convex domains

Guofang Wang; Chao Xia

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arXiv · 1112.4398

An optimal anisotropic Poincaré inequality for convex domains

Guofang Wang·Chao Xia

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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.

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Guofang Wang, Chao Xia. 2011-12-19. An optimal anisotropic Poincaré inequality for convex domains. https://arxiv.org/abs/1112.4398

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