An optimal anisotropic Poincaré inequality for convex domains

By Guofang Wang, Chao Xia. 2011

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In this paper, we prove a sharp lower bound of the first (nonzero) eigenvalue of the anisotropic Laplacian with the Neumann boundary condition. Equivalently, we prove an optimal anisotropic Poincare inequality for convex domains, which generalizes the classical result of Payne and Weinberger. A lower bound of the first (nonzero) eigenvalue of the anisotropic Laplacian with the Dirichlet boundary condition is also proved.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/7a0053d06ce2977e5716aa1d21aecbeeb9941338