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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.08393 |
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| _version_ | 1866911259597733888 |
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| author | Engelstein, Max Restrepo, Daniel Zhao, Zihui |
| author_facet | Engelstein, Max Restrepo, Daniel Zhao, Zihui |
| contents | In this article we study the structure of solutions to the one-phase Bernoulli problem that are modeled either infinitesimally or at infinity by one-homogeneous solutions with an isolated singularity. In particular, we prove a uniqueness of blowups result under a natural symmetry condition on the one-homogeneous solution (à la Allard--Almgren) and we prove a rigidity result at infinity (à la Simon--Solomon) under additional constraints on the linearized operator around the one-homogeneous solution (which are satisfied by the only known examples of minimizing one-homogeneous solutions). We believe these are the first uniqueness of blow-up/blow-down results at singular points for non-minimizing solutions to the one-phase problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08393 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the asymptotic properties of solutions to one-phase free boundary problems Engelstein, Max Restrepo, Daniel Zhao, Zihui Analysis of PDEs Differential Geometry In this article we study the structure of solutions to the one-phase Bernoulli problem that are modeled either infinitesimally or at infinity by one-homogeneous solutions with an isolated singularity. In particular, we prove a uniqueness of blowups result under a natural symmetry condition on the one-homogeneous solution (à la Allard--Almgren) and we prove a rigidity result at infinity (à la Simon--Solomon) under additional constraints on the linearized operator around the one-homogeneous solution (which are satisfied by the only known examples of minimizing one-homogeneous solutions). We believe these are the first uniqueness of blow-up/blow-down results at singular points for non-minimizing solutions to the one-phase problem. |
| title | On the asymptotic properties of solutions to one-phase free boundary problems |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2511.08393 |