关于对数Sobolev常数的估计

ON ESTIMATION OF LOGARITHMIC SOBOLEV CONSTANT

研究紧Ｒｉｅｍａｎｎ流形上可逆扩散过程对数Ｓｏｂｏｌｅｖ常数的估计，所获结果在一些有意义情形（特别是负曲率下界情形）优于Ｄｅｕｓｃｈｅｌ－Ｓｔｒｏｏｃｋ的估计，此外，对带边紧流形上的扩散过程，也给出了相同的估计。

Estimation of logarithmic Sobolev constant for reveisible diffusion processes on compact Riemannian manifolds is studied.The resulting estimates improves Deuschel-Strock's estimate for some interesting cases,especially for manifolds with negative lower bound of Ricci curvature.Finally,the same estimates are also proved for reflecting diffusion processes on manifold with boundary.