AN OPTIMAL ANISOTROPIC POINCARE INEQUALITY FOR CONVEX DOMAINS

作者：Wang Guofang^*; Xia Chao

来源：Pacific Journal of Mathematics, 2012, 258(2): 305-326.

DOI：10.2140/pjm.2012.258.305

• anisotropic Laplacian
• first eigenvalue
• gradient estimate
• optimal Poincare inequality

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.

• 出版日期2012-8