Heat semigroup and functions of bounded variation on Riemannian manifolds
Heat semigroup and functions of bounded variation on Riemannian manifolds
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热半群和黎曼流形上的有界变分函数
DOI：
10.1515/crelle.2007.093
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
M. Preunkert
中科院分区：
文献类型：
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作者：
M. Miranda;D. Pallara;F. Paronetto;M. Preunkert
抽象让M与里奇没有边界的连接黎曼流形曲率有界从下面这样的测地线球的体积的中心和固定半径为r > 0卷有界远离0统一对x,并让(T (T)) T≧0是热半群M .我们显示的总变异函数的梯度u∈L 1 (M)等于极限的L 1-norm∇T→0时T (T) u。特别地，当且仅当u是有界变化的函数时，这个极限是有限的。
Abstract Let M be a connected Riemannian manifold without boundary with Ricci curvature bounded from below and such that the volume of the geodesic balls of centre x and fixed radius r > 0 have a volume bounded away from 0 uniformly with respect to x, and let (T(t)) t≧0 be the heat semigroup on M. We show that the total variation of the gradient of a function u ∈ L 1(M) equals the limit of the L 1-norm of ∇T(t)u as t → 0. In particular, this limit is finite if and only if u is a function of bounded variation.