Homogenisation of nonlinear Dirichlet problems in randomly perforated domains under minimal assumptions on the size of perforations

• 成果类型: Article
• 署名作者: Scardia, Lucia; Zemas, Konstantinos; Zeppieri, Caterina Ida
• 署名单位: Heriot Watt University; University of Bonn; University of Munster
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01320-1
• 发表日期: 2025
• 页码: 471-544
• 关键词: ASYMPTOTIC-BEHAVIOR; Poisson equation

摘要

In this paper we study the convergence of nonlinear Dirichlet problems for systems of variational elliptic PDEs defined on randomly perforated domains of R-n. Under the assumption that the perforations are small balls whose centres and radii are generated by a stationary short-range marked point process, we obtain in the critical-scaling limit an averaged nonlinear analogue of the extra term obtained in the classical work of Cioranescu and Murat (Res Notes Math III, 1982). In analogy to the random setting recently introduced by Giunti, Hofer and Velazquez (Commun Part Differ Equ43(9):1377-1412, 2018) to study the Poisson equation, we only require that the random radii have finite(n-q)-moment, where 1