The main result of this paper is that when the coefficients of the time-dependent divergence form operators are Hlder continuous in time with order not too much smaller than （1/2）,the distance of the semigroups of t...The main result of this paper is that when the coefficients of the time-dependent divergence form operators are Hlder continuous in time with order not too much smaller than （1/2）,the distance of the semigroups of two operators is bounded by the L<sub>2</sub> distance of the coefficients of their corresponding operators.展开更多
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 con...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.展开更多
基金Research partially supported by N.S.F.Grants DMS-9625642
文摘The main result of this paper is that when the coefficients of the time-dependent divergence form operators are Hlder continuous in time with order not too much smaller than （1/2）,the distance of the semigroups of two operators is bounded by the L<sub>2</sub> distance of the coefficients of their corresponding operators.
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)
文摘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.
