Quantitative stratification for the fractional Allen-Cahn equation and stationary nonlocal minimal surface
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916658910593024 |
|---|---|
| author | Wang, Kelei Wei, Juncheng Wu, Ke |
| author_facet | Wang, Kelei Wei, Juncheng Wu, Ke |
| contents | We study properties of solutions to the fractional Allen-Cahn equation when $s\in (0, 1/2)$ and dimension $n\geq 2$. By applying the quantitative stratification principle developed by Naber and Valtorta, we obtain an optimal quantitative estimate on the transition set. As an application of this estimate, we improve the potential energy estimates of Cabre, Cinti, and Serra (2021), providing sharp versions for the fractional Allen-Cahn equation. Similarly, we obtain optimal perimeter estimates for stationary nonlocal minimal surfaces, extending previous results of Cinti, Serra, and Valdinoci (2019) from the stable case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16829 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative stratification for the fractional Allen-Cahn equation and stationary nonlocal minimal surface Wang, Kelei Wei, Juncheng Wu, Ke Analysis of PDEs Differential Geometry We study properties of solutions to the fractional Allen-Cahn equation when $s\in (0, 1/2)$ and dimension $n\geq 2$. By applying the quantitative stratification principle developed by Naber and Valtorta, we obtain an optimal quantitative estimate on the transition set. As an application of this estimate, we improve the potential energy estimates of Cabre, Cinti, and Serra (2021), providing sharp versions for the fractional Allen-Cahn equation. Similarly, we obtain optimal perimeter estimates for stationary nonlocal minimal surfaces, extending previous results of Cinti, Serra, and Valdinoci (2019) from the stable case. |
| title | Quantitative stratification for the fractional Allen-Cahn equation and stationary nonlocal minimal surface |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2503.16829 |