Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.05603 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913348738613248 |
|---|---|
| author | Novack, Michael |
| author_facet | Novack, Michael |
| contents | We study a variational model for soap films in which the films are represented by sets with fixed small volume rather than surfaces. In this problem, a minimizing sequence of completely "wet" films, or sets of finite perimeter spanning a wire frame, may converge to a film containing both wet regions of positive volume and collapsed (dry) surfaces. When collapsing occurs, these limiting objects lie outside the original minimization class and instead are admissible for a relaxed problem. Here we show that the relaxation and the original formulation are equivalent by approximating the collapsed films in the relaxed class by wet films in the original class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_05603 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the relaxation of Gauss's capillarity theory under spanning conditions Novack, Michael Analysis of PDEs We study a variational model for soap films in which the films are represented by sets with fixed small volume rather than surfaces. In this problem, a minimizing sequence of completely "wet" films, or sets of finite perimeter spanning a wire frame, may converge to a film containing both wet regions of positive volume and collapsed (dry) surfaces. When collapsing occurs, these limiting objects lie outside the original minimization class and instead are admissible for a relaxed problem. Here we show that the relaxation and the original formulation are equivalent by approximating the collapsed films in the relaxed class by wet films in the original class. |
| title | On the relaxation of Gauss's capillarity theory under spanning conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2311.05603 |