Dirichlet forms on unconstrained Sierpinski carpets

• 成果类型: Article
• 署名作者: Cao, Shiping; Qiu, Hua
• 署名单位: University of Washington; University of Washington Seattle; Nanjing University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01280-6
• 发表日期: 2024
• 页码: 613-657
• 关键词: brownian-motion; trace theorem; fractals; uniqueness; laplacians

摘要

We construct symmetric self-similar Dirichlet forms on unconstrained Sierpinski carpets, which are natural extension of planar Sierpinski carpets by allowing the small cells to live off the 1/k grids. The intersection of two cells can be a line segment of irrational length, and the non-diagonal assumption is dropped in this recurrent setting.