摘要
By establishing the intrinsic super-Poincar'e inequality,some explicit conditions are presented for diffusion semigroups on a non-compact complete Riemannian manifold to be intrinsically ultracontractive.These conditions,as well as the resulting uniform upper bounds on the intrinsic heat kernels,are sharp for some concrete examples.
By establishing the intrinsic super-Poincar’e inequality,some explicit conditions are presented for diffusion semigroups on a non-compact complete Riemannian manifold to be intrinsically ultracontractive.These conditions,as well as the resulting uniform upper bounds on the intrinsic heat kernels,are sharp for some concrete examples.
基金
supported by Science Fund for Creative Research Groups of National Natural Science Foundation of China (No.10121101)
National Basic Research Program of China(Grant No.2006CB805901)
