Classification of blow-ups for the Alt--Phillips problem in three dimensions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911735733026816 |
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| author | Fernández-Real, Xavier |
| author_facet | Fernández-Real, Xavier |
| contents | We prove a flatness theorem for classical stable homogeneous solutions of the $γ$-Alt--Phillips free boundary problem in three dimensions in the range $0<γ\le 2/3$, where $γ$ is the exponent in the energy density $|\nabla u|^2+u^γ$. In particular, this implies full regularity of the free boundary for minimizers of the corresponding Alt--Phillips energy in dimension $3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00538 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of blow-ups for the Alt--Phillips problem in three dimensions Fernández-Real, Xavier Analysis of PDEs 35R35, 35B08, 35J61, 35B65 We prove a flatness theorem for classical stable homogeneous solutions of the $γ$-Alt--Phillips free boundary problem in three dimensions in the range $0<γ\le 2/3$, where $γ$ is the exponent in the energy density $|\nabla u|^2+u^γ$. In particular, this implies full regularity of the free boundary for minimizers of the corresponding Alt--Phillips energy in dimension $3$. |
| title | Classification of blow-ups for the Alt--Phillips problem in three dimensions |
| topic | Analysis of PDEs 35R35, 35B08, 35J61, 35B65 |
| url | https://arxiv.org/abs/2606.00538 |