$Γ$-convergence of the non-local Massari functional and applications to inhomogeneous Allen-Cahn equations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915996719120384 |
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| author | Dipierro, Serena Valdinoci, Enrico Villa, Riccardo |
| author_facet | Dipierro, Serena Valdinoci, Enrico Villa, Riccardo |
| contents | We present several asymptotic results concerning the non-local Massari Problem for sets with prescribed mean curvature. In particular, we show that the fractional Massari functional $Γ$-converges to the classical one, and this convergence preserves minimizers in the $L^1_{\mbox{loc}}$-topology. This returns useful information about the asymptotic behavior of the solutions of the inhomogeneous Allen-Cahn equation in the forced and the mass-prescribed settings. In this context, a new geometric object, which we refer to as "non-local hybrid mean curvature", naturally appears. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $Γ$-convergence of the non-local Massari functional and applications to inhomogeneous Allen-Cahn equations Dipierro, Serena Valdinoci, Enrico Villa, Riccardo Analysis of PDEs We present several asymptotic results concerning the non-local Massari Problem for sets with prescribed mean curvature. In particular, we show that the fractional Massari functional $Γ$-converges to the classical one, and this convergence preserves minimizers in the $L^1_{\mbox{loc}}$-topology. This returns useful information about the asymptotic behavior of the solutions of the inhomogeneous Allen-Cahn equation in the forced and the mass-prescribed settings. In this context, a new geometric object, which we refer to as "non-local hybrid mean curvature", naturally appears. |
| title | $Γ$-convergence of the non-local Massari functional and applications to inhomogeneous Allen-Cahn equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.15946 |