The planar Plateau's problem via capillarity
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912073843212288 |
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| author | Idu, Kennedy Obinna |
| author_facet | Idu, Kennedy Obinna |
| contents | The Plateau's problem seeks to determine a surface of minimal area which spans a given boundary. It is widely studied for its varied mathematical formulations, applications and relevance to physical models such as soap films. We revisit the problem and study a soap film model in the spirit of capillarity formulations in two dimensions. Our approach introduces a nonlocal geometric potential in the variational length minimization scheme. This incorporates effects of thickness of soap films and provides insight into addressing the so-called collapsing phenomenon and other observable physical phenomena and properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12131 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The planar Plateau's problem via capillarity Idu, Kennedy Obinna Classical Analysis and ODEs Analysis of PDEs 49Q05, 53A10, 49Q20 The Plateau's problem seeks to determine a surface of minimal area which spans a given boundary. It is widely studied for its varied mathematical formulations, applications and relevance to physical models such as soap films. We revisit the problem and study a soap film model in the spirit of capillarity formulations in two dimensions. Our approach introduces a nonlocal geometric potential in the variational length minimization scheme. This incorporates effects of thickness of soap films and provides insight into addressing the so-called collapsing phenomenon and other observable physical phenomena and properties. |
| title | The planar Plateau's problem via capillarity |
| topic | Classical Analysis and ODEs Analysis of PDEs 49Q05, 53A10, 49Q20 |
| url | https://arxiv.org/abs/2410.12131 |