A stability inequality for the planar lens partition
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916583190822912 |
|---|---|
| author | Bonacini, Marco Cristoferi, Riccardo Topaloglu, Ihsan |
| author_facet | Bonacini, Marco Cristoferi, Riccardo Topaloglu, Ihsan |
| contents | Recently it has been shown that the unique locally perimeter minimizing partitioning of the plane into three regions, where one region has finite area and the other two have infinite measure, is given by the so-called standard lens partition. Here we prove a sharp stability inequality for the standard lens; hence strengthening the local minimality of the lens partition in a quantitative form. As an application of this stability result we consider a nonlocal perturbation of an isoperimetric problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21677 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A stability inequality for the planar lens partition Bonacini, Marco Cristoferi, Riccardo Topaloglu, Ihsan Analysis of PDEs Recently it has been shown that the unique locally perimeter minimizing partitioning of the plane into three regions, where one region has finite area and the other two have infinite measure, is given by the so-called standard lens partition. Here we prove a sharp stability inequality for the standard lens; hence strengthening the local minimality of the lens partition in a quantitative form. As an application of this stability result we consider a nonlocal perturbation of an isoperimetric problem. |
| title | A stability inequality for the planar lens partition |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.21677 |