Nonlocal Phase Transitions with Singular Heterogeneous Kernels
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912085803270144 |
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| author | Caldwell, Wes |
| author_facet | Caldwell, Wes |
| contents | In this paper the study of a non-local Cahn-Hilliard-type singularly perturbed family of functionals is undertaken, generalizing known results by Alberti & Bellettini. The kernels considered include those leading to Gagliardo seminorms for fractional Sobolev spaces. The limit energy is computed via $Γ$-convergence and shown to be an anisotropic surface energy on the interface between the two phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19624 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlocal Phase Transitions with Singular Heterogeneous Kernels Caldwell, Wes Analysis of PDEs 49J45 In this paper the study of a non-local Cahn-Hilliard-type singularly perturbed family of functionals is undertaken, generalizing known results by Alberti & Bellettini. The kernels considered include those leading to Gagliardo seminorms for fractional Sobolev spaces. The limit energy is computed via $Γ$-convergence and shown to be an anisotropic surface energy on the interface between the two phases. |
| title | Nonlocal Phase Transitions with Singular Heterogeneous Kernels |
| topic | Analysis of PDEs 49J45 |
| url | https://arxiv.org/abs/2410.19624 |