Lagrangian flows driven by fields in Wiener spaces

• 成果类型: Article
• 署名作者: Trevisan, Dario
• 署名单位: Scuola Normale Superiore di Pisa
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0589-1
• 发表日期: 2015
• 页码: 123-147
• 关键词: ordinary differential-equations; planck type equations; vector-fields; bv functions; infinite dimensions; transport-equation; cauchy-problem; diperna-lions; uniqueness; EXISTENCE

摘要

We establish the renormalization property for essentially bounded solutions of the continuity equation associated to bounded variation () fields in Wiener spaces, with values in the associated Cameron-Martin space; thus obtaining, by standard arguments, new uniqueness and stability results for correspondent Lagrangian flows.