Heteroclinic connections for fractional Allen-Cahn equations with degenerate potentials
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913859647832064 |
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| author | De Pas, Francesco Dipierro, Serena Piccinini, Mirco Valdinoci, Enrico |
| author_facet | De Pas, Francesco Dipierro, Serena Piccinini, Mirco Valdinoci, Enrico |
| contents | We investigate existence, uniqueness and asymptotic behavior of minimizers of a family of non-local energy functionals of the type $$
\frac{1}{4}\iint_{\mathbb{R}^{2n}\setminus (\mathbb{R}^n \setminus Ω)^2}|u(x)-u(y)|^2 K(x-y) \,dx dy + \int_ΩW(u(x)) \,dx. $$
Here, $W$ is a possibly degenerate double well potential with a polynomial control on its second derivative near the wells. Also, ${K}$ belongs to a wide class of measurable kernels and is modeled on that of the fractional Laplacian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20054 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heteroclinic connections for fractional Allen-Cahn equations with degenerate potentials De Pas, Francesco Dipierro, Serena Piccinini, Mirco Valdinoci, Enrico Analysis of PDEs We investigate existence, uniqueness and asymptotic behavior of minimizers of a family of non-local energy functionals of the type $$ \frac{1}{4}\iint_{\mathbb{R}^{2n}\setminus (\mathbb{R}^n \setminus Ω)^2}|u(x)-u(y)|^2 K(x-y) \,dx dy + \int_ΩW(u(x)) \,dx. $$ Here, $W$ is a possibly degenerate double well potential with a polynomial control on its second derivative near the wells. Also, ${K}$ belongs to a wide class of measurable kernels and is modeled on that of the fractional Laplacian. |
| title | Heteroclinic connections for fractional Allen-Cahn equations with degenerate potentials |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.20054 |