Heat kernels and maximal l<sup>p</sup>—l<sup>q</sup>estimates for parabolic evolution equations 论文
1997Communications in Partial Differential Equations引用 291
Advanced Mathematical Modeling in EngineeringStability and Controllability of Differential EquationsNumerical methods in inverse problems
摘要
Let A be the generator of an analytic semigroup Ton L2(Ω), where Ω is a homogeneous space with doubling property. We prove maximal Lp-Lp a—priori estimates for the solution of the parabolic evolution equation u'(t)=Au(t)+f(t), u(0)=0 provided Tmay be represented by a heat—kernel satisfying certain bounds (and in particular a Gaussian bound). 1991 Mathematics Subject Classification:35K22, 58D25, 47D06