Uniform stability in the Euclidean isoperimetric problem for the Allen--Cahn energy
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866911931076444160 |
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| author | Maggi, Francesco Restrepo, Daniel |
| author_facet | Maggi, Francesco Restrepo, Daniel |
| contents | We consider the isoperimetric problem defined on the whole $\mathbb{R}^n$ by the Allen--Cahn energy functional. For non-degenerate double well potentials, we prove sharp quantitative stability inequalities of quadratic type which are uniform in the length scale of the phase transitions. We also derive a rigidity theorem for critical points analogous to the classical Alexandrov's theorem for constant mean curvature boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_11583 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Uniform stability in the Euclidean isoperimetric problem for the Allen--Cahn energy Maggi, Francesco Restrepo, Daniel Analysis of PDEs Mathematical Physics Optimization and Control We consider the isoperimetric problem defined on the whole $\mathbb{R}^n$ by the Allen--Cahn energy functional. For non-degenerate double well potentials, we prove sharp quantitative stability inequalities of quadratic type which are uniform in the length scale of the phase transitions. We also derive a rigidity theorem for critical points analogous to the classical Alexandrov's theorem for constant mean curvature boundaries. |
| title | Uniform stability in the Euclidean isoperimetric problem for the Allen--Cahn energy |
| topic | Analysis of PDEs Mathematical Physics Optimization and Control |
| url | https://arxiv.org/abs/2202.11583 |