Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators
Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators
复制标题
DOI：
10.1007/bfb0103045
复制
发表时间：
2000-04
期刊：
影响因子：
--
通讯作者：
A. Eberle
中科院分区：
文献类型：
--
作者：
A. Eberle
本书面向研究扩散过程的概率学家和对具有奇异系数的线性抛物型偏微分方程感兴趣的分析师。讨论的核心问题是给定的扩散算子，即没有零阶项的二阶线性微分算子，仅在某些（有限或无限维）状态空间上的测试函数上先验定义，是否唯一确定相应加权 Lp 空间上的强连续半群。特别强调导致非唯一性的现象，以及分析和概率背景中出现的不同唯一性概念之间的关系。
This book addresses both probabilists working on diffusion processes and analysts interested in linear parabolic partial differential equations with singular coefficients. The central question discussed is whether a given diffusion operator, ie, a second order linear differential operator without zeroth order term, which is a priori defined on test functions over some (finite or infinite dimensional) state space only, uniquely determines a strongly continuous semigroup on a corresponding weighted Lp space. Particular emphasis is placed on phenomena causing non-uniqueness, as well as on the relation between different notions of uniqueness appearing in analytic and probabilistic contexts.