Nonlocal-interaction vortices
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912422791479296 |
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| author | Solci, Margherita |
| author_facet | Solci, Margherita |
| contents | We consider sequences of quadratic non-local functionals, depending on a small parameter $\e$, that approximate the Dirichlet integral by a well-known result by Bourgain, Brezis and Mironescu. Similarly to what is done for hard-core approximations to vortex energies in the case of the Dirichlet integral, we further scale such energies by $|\log\e|^{-1}$ and restrict them to $S^1$-valued functions. We introduce a notion of convergence of functions to integral currents with respect to which such energies are equi-coercive, and show the converge to a vortex energy, similarly to the limit behaviour of Ginzburg-Landau energies at the vortex scaling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06526 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonlocal-interaction vortices Solci, Margherita Analysis of PDEs Mathematical Physics 49J45, 35Q56, 74A70, 46E39 We consider sequences of quadratic non-local functionals, depending on a small parameter $\e$, that approximate the Dirichlet integral by a well-known result by Bourgain, Brezis and Mironescu. Similarly to what is done for hard-core approximations to vortex energies in the case of the Dirichlet integral, we further scale such energies by $|\log\e|^{-1}$ and restrict them to $S^1$-valued functions. We introduce a notion of convergence of functions to integral currents with respect to which such energies are equi-coercive, and show the converge to a vortex energy, similarly to the limit behaviour of Ginzburg-Landau energies at the vortex scaling. |
| title | Nonlocal-interaction vortices |
| topic | Analysis of PDEs Mathematical Physics 49J45, 35Q56, 74A70, 46E39 |
| url | https://arxiv.org/abs/2302.06526 |