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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.03553 |
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| _version_ | 1866911648302759936 |
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| author | Sepúlveda, Sebastián Flores Niethammer, Barbara Velázquez, Juan J. L. |
| author_facet | Sepúlveda, Sebastián Flores Niethammer, Barbara Velázquez, Juan J. L. |
| contents | In this paper we study a mass-constrained free boundary problem modeling cell polarization, in the regime where the mass is small. In the generic case of a signal with nondegenerate maxima, we prove that the solution converges locally to a global, integrable solution to an obstacle problem in the plane. We further show that the interface of the solution to the limit problem is an ellipse, the equation of which is explicit. We also study some cases where the signal has degenerate maxima, highlighting a variety of possible behaviors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the shape of the positivity region for a free boundary problem describing cell polarization Sepúlveda, Sebastián Flores Niethammer, Barbara Velázquez, Juan J. L. Analysis of PDEs In this paper we study a mass-constrained free boundary problem modeling cell polarization, in the regime where the mass is small. In the generic case of a signal with nondegenerate maxima, we prove that the solution converges locally to a global, integrable solution to an obstacle problem in the plane. We further show that the interface of the solution to the limit problem is an ellipse, the equation of which is explicit. We also study some cases where the signal has degenerate maxima, highlighting a variety of possible behaviors. |
| title | On the shape of the positivity region for a free boundary problem describing cell polarization |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.03553 |