Bifurcations in Isoperimetric Problems with Nonlocal Interactions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918459247427584 |
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| author | De Regibus, Fabio Grossi, Massimo Musso, Monica |
| author_facet | De Regibus, Fabio Grossi, Massimo Musso, Monica |
| contents | We study isoperimetric problems modeled on the liquid drop model, with nonlocal interactions under a volume constraint. While balls are natural critical points, we show that, for an unbounded sequence of radii, non-spherical solutions bifurcate from the family of balls. These new solutions lie arbitrarily close to balls and can have arbitrarily large volume. Conversely, at radii outside this sequence, no bifurcation occurs, and nearby solutions are trivial, arising only from rigid motions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19170 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bifurcations in Isoperimetric Problems with Nonlocal Interactions De Regibus, Fabio Grossi, Massimo Musso, Monica Analysis of PDEs We study isoperimetric problems modeled on the liquid drop model, with nonlocal interactions under a volume constraint. While balls are natural critical points, we show that, for an unbounded sequence of radii, non-spherical solutions bifurcate from the family of balls. These new solutions lie arbitrarily close to balls and can have arbitrarily large volume. Conversely, at radii outside this sequence, no bifurcation occurs, and nearby solutions are trivial, arising only from rigid motions. |
| title | Bifurcations in Isoperimetric Problems with Nonlocal Interactions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.19170 |