Stability inequalities for one-phase cones
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918302488461312 |
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| author | Firester, Benjy Tsiamis, Raphael Wang, Yipeng |
| author_facet | Firester, Benjy Tsiamis, Raphael Wang, Yipeng |
| contents | We obtain strict stability inequalities for homogeneous solutions of the one-phase Bernoulli problem. We prove that in dimension $7$ and above, cohomogeneity one solutions with bi-orthogonal symmetry are strictly stable. As a consequence, we obtain a bound on the first eigenvalue and the decay rates of Jacobi fields, with applications to the generic regularity of the one-phase problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16966 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stability inequalities for one-phase cones Firester, Benjy Tsiamis, Raphael Wang, Yipeng Analysis of PDEs Differential Geometry We obtain strict stability inequalities for homogeneous solutions of the one-phase Bernoulli problem. We prove that in dimension $7$ and above, cohomogeneity one solutions with bi-orthogonal symmetry are strictly stable. As a consequence, we obtain a bound on the first eigenvalue and the decay rates of Jacobi fields, with applications to the generic regularity of the one-phase problem. |
| title | Stability inequalities for one-phase cones |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2601.16966 |