A Regularity Theory for Stationary Two-valued Harmonic Functions
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912378549960704 |
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| author | Cheng, Lingxiao Wang, Lubo |
| author_facet | Cheng, Lingxiao Wang, Lubo |
| contents | For stationary two-valued harmonic functions with Hölder regularity, we establish their Lipschitz regularity and prove that the nodal set consists of analytic hypersurfaces away from a singular set. The main tools are the Almgren monotonicity formula and the blow-up method. These results are applicable to some limiting problems in segregation models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Regularity Theory for Stationary Two-valued Harmonic Functions Cheng, Lingxiao Wang, Lubo Analysis of PDEs For stationary two-valued harmonic functions with Hölder regularity, we establish their Lipschitz regularity and prove that the nodal set consists of analytic hypersurfaces away from a singular set. The main tools are the Almgren monotonicity formula and the blow-up method. These results are applicable to some limiting problems in segregation models. |
| title | A Regularity Theory for Stationary Two-valued Harmonic Functions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.23318 |