Estimation of spectral gap for elliptic operators

A variational formula for the lower bound of the spectral gap of an elliptic operator is presented in the paper for the first time. The main known results are either recovered or improved. A large number of new examples with sharp estimate are illustrated. Moreover, as an application of the march coupling, the Poincare inequality with respect to the absolute distribution of the process is also studied.

[1]  Feng-Yu Wang,et al.  Estimates of Logarithmic Sobolev Constant: An Improvement of Bakry–Emery Criterion , 1997 .

[2]  Mu-Fa Chen,et al.  Estimation of the First Eigenvalue of Second Order Elliptic Operators , 1995 .

[3]  F. Wang.  Gradient Estimates on Rd , 1994, Canadian Mathematical Bulletin.

[4]  C. Mufa,et al.  Optimal markovian couplings and applications , 1994 .

[5]  Feng-Yu Wang.  Application of coupling methods to the Neumann eigenvalue problem , 1994 .

[6]  Mu-Fa Chen,et al.  On order-preservation and positive correlations for multidimensional diffusion processes , 1993 .

[7]  Mu-Fa Chen,et al.  From Markov Chains to Non-Equilibrium Particle Systems , 1992 .

[8]  Thomas M. Liggett,et al.  Exponential $L_2$ Convergence of Attractive Reversible Nearest Particle Systems , 1989 .

[9]  L. Rogers,et al.  Coupling of Multidimensional Diffusions by Reflection , 1986 .

[10]  Elton P. Hsu.  Logarithmic Sobolev Inequalities on Path Spaces Over Riemannian Manifolds , 1997 .

[11]  F. Wang.  Logarithmic Sobolev inequalities for diffusion Processes with application to path space , 1996 .

[12]  Wang Fengyu.  Application of coupling method to the first eigenvalue on manifold , 1995 .

[13]  E. Hsu.  Inégalités de Sobolev logarithmiques sur un espace de chemins , 1995 .

[14]  Wang Fengyu.  Spectral gap for diffusion processes on noncompact manifolds , 1995 .

[15]  Chen Mu.  Application of Coupling Method to the First Eigenvalue on Manifold , 1994 .

[16]  Mu-Fa Chen,et al.  Coupling Methods for Multidimensional Diffusion Processes , 1989 .

[17]  I. Chavel.  Eigenvalues in Riemannian geometry , 1984 .

[18]  S. Watanabe,et al.  Krein's spectral theory of strings and generalized diffusion processes , 1982 .