Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.10918 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910083583049728 |
|---|---|
| author | Cicalese, Marco Kreutz, Leonard Mansoor, Imteyaz |
| author_facet | Cicalese, Marco Kreutz, Leonard Mansoor, Imteyaz |
| contents | The classical isocapacitary inequality states that, among all sets of fixed volume, the ball uniquely minimizes the capacity. While this result holds in the continuum, it fails in the discrete setting, where the isocapacitary problem may admit multiple minimizers. In this paper we establish quantitative fluctuation estimates for the discrete isocapacitary problem on subsets of $\mathbb{Z}^d$
as their cardinality diverges. Our approach relies on a careful extension of the associated variational problem from the discrete to the continuum setting, combined with sharp (continuum) quantitative isocapacitary inequalities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10918 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discrete Quantitative Isocapacitary Inequality: Fluctuation Estimates Cicalese, Marco Kreutz, Leonard Mansoor, Imteyaz Analysis of PDEs The classical isocapacitary inequality states that, among all sets of fixed volume, the ball uniquely minimizes the capacity. While this result holds in the continuum, it fails in the discrete setting, where the isocapacitary problem may admit multiple minimizers. In this paper we establish quantitative fluctuation estimates for the discrete isocapacitary problem on subsets of $\mathbb{Z}^d$ as their cardinality diverges. Our approach relies on a careful extension of the associated variational problem from the discrete to the continuum setting, combined with sharp (continuum) quantitative isocapacitary inequalities. |
| title | Discrete Quantitative Isocapacitary Inequality: Fluctuation Estimates |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.10918 |