Concentration of cones in the Alt-Phillips problem
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913105144971264 |
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| author | Savin, Ovidiu Yu, Hui |
| author_facet | Savin, Ovidiu Yu, Hui |
| contents | We study minimizing cones in the Alt-Phillips problem when the exponent γ is close to 1.
When γ converges to 1, we show that the cones concentrate around symmetric solutions to the classical obstacle problem. To be precise, the limiting profiles are radial in a subspace and invariant in directions perpendicular to that subspace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03626 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Concentration of cones in the Alt-Phillips problem Savin, Ovidiu Yu, Hui Analysis of PDEs We study minimizing cones in the Alt-Phillips problem when the exponent γ is close to 1. When γ converges to 1, we show that the cones concentrate around symmetric solutions to the classical obstacle problem. To be precise, the limiting profiles are radial in a subspace and invariant in directions perpendicular to that subspace. |
| title | Concentration of cones in the Alt-Phillips problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.03626 |