Long-range phase coexistence models with degenerate potentials
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911586871934976 |
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| author | De Pas, Francesco Dipierro, Serena Valdinoci, Enrico |
| author_facet | De Pas, Francesco Dipierro, Serena Valdinoci, Enrico |
| contents | This survey offers an overview of recent advances in nonlocal phase transition problems, modeled by Ginzburg--Landau type energies of the form \[ \frac{1}{4}\iint_{\R^{2n}\setminus (\R^n \setminus Ω)^2} \frac{|u(x)-u(y)|^2}{|x-y|^{n+2s}}\,dx\,dy \;+\; \int_ΩW(u(x))\,dx. \] Here,~$W$ is a smooth and possibly \textit{degenerate} double well potential, with a polynomial control on its second derivatives near the wells. The emphasis is on qualitative properties of minimizers and critical points of the energy functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10909 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Long-range phase coexistence models with degenerate potentials De Pas, Francesco Dipierro, Serena Valdinoci, Enrico Analysis of PDEs This survey offers an overview of recent advances in nonlocal phase transition problems, modeled by Ginzburg--Landau type energies of the form \[ \frac{1}{4}\iint_{\R^{2n}\setminus (\R^n \setminus Ω)^2} \frac{|u(x)-u(y)|^2}{|x-y|^{n+2s}}\,dx\,dy \;+\; \int_ΩW(u(x))\,dx. \] Here,~$W$ is a smooth and possibly \textit{degenerate} double well potential, with a polynomial control on its second derivatives near the wells. The emphasis is on qualitative properties of minimizers and critical points of the energy functional. |
| title | Long-range phase coexistence models with degenerate potentials |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.10909 |