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On functions of bounded variation on convex domains in Hilbert spaces
Journal of Evolution Equations ( IF 1.4 ) Pub Date : 2021-03-11 , DOI: 10.1007/s00028-021-00680-8 Luciana Angiuli , Simone Ferrari , Diego Pallara
中文翻译:
关于希尔伯特空间中凸域上的有界变化函数
更新日期:2021-03-11
Journal of Evolution Equations ( IF 1.4 ) Pub Date : 2021-03-11 , DOI: 10.1007/s00028-021-00680-8 Luciana Angiuli , Simone Ferrari , Diego Pallara
We study functions of bounded variation (and sets of finite perimeter) on a convex open set \({\varOmega }\subseteq X\), X being an infinite-dimensional separable real Hilbert space. We relate the total variation of such functions, defined through an integration by parts formula, to the short-time behaviour of the semigroup associated with a perturbation of the Ornstein–Uhlenbeck operator.
中文翻译:
关于希尔伯特空间中凸域上的有界变化函数
我们研究凸开放集\({\ varOmega} \ subseteq X \)上的有界变化(和有限周长集)的函数,X是无限维可分离的实Hilbert空间。我们将这些函数的总变化(通过零件公式积分来定义)与半群的短时行为联系起来,该半群与Ornstein–Uhlenbeck算子的扰动有关。