BV functions and sets of finite perimeter on configuration spaces

Brué, Elia; Suzuki, Kohei

Abstract

In this paper, we aim to develop the foundations of a theory of BV functions in the configuration space over the Euclidean space Rn equipped with the Poisson measure π. We first construct the m-codimensional Poisson measure—formally written as “(∞-m)-dimensional Poisson measure”—on the configuration space. We then show that our construction is consistent with potential theory induced by the infinitely many independent Brownian motions by establishing relations between the m-codimensional Poisson measure and Bessel capacities. Secondly, we introduce three different definitions of BV functions based on the variational, relaxation, and semigroup approaches, and prove the equivalence of them. In the process, we prove the p-Bakry–Émery inequality on the configuration space for any 1

Citation

Brué, E., & Suzuki, K. (2025). BV functions and sets of finite perimeter on configuration spaces. Calculus of Variations and Partial Differential Equations, 64(6), Article 177. https://doi.org/10.1007/s00526-025-03015-4

• Journal Article Type: Article
• Acceptance Date: Apr 25, 2025
• Online Publication Date: May 30, 2025
• Publication Date: 2025-07
• Deposit Date: Jun 2, 2025
• Publicly Available Date: Jun 2, 2025
• Journal: Calculus of Variations and Partial Differential Equations
• Print ISSN: 0944-2669
• Electronic ISSN: 1432-0835
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 64
• Issue: 6
• Article Number: 177
• DOI: https://doi.org/10.1007/s00526-025-03015-4
• Keywords: 28A78, 26E15, Secondary 28A75, Primary 28C20
• Public URL: https://durham-repository.worktribe.com/output/3967762