Topological singularities arising from fractional-gradient energies
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914796248498176 |
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| author | Alicandro, Roberto Braides, Andrea Solci, Margherita Stefani, Giorgio |
| author_facet | Alicandro, Roberto Braides, Andrea Solci, Margherita Stefani, Giorgio |
| contents | We prove that, on a planar regular domain, suitably scaled functionals of Ginzburg-Landau type, given by the sum of quadratic fractional Sobolev seminorms and a penalization term vanishing on the unitary sphere, $Γ$-converge to vortex-type energies with respect to the flat convergence of Jacobians. The compactness and the $Γ$-$\liminf$ follow by comparison with standard Ginzburg-Landau functionals depending on Riesz potentials. The $Γ$-$\limsup$, instead, is achieved via a direct argument by joining a finite number of vortex-like functions suitably truncated around the singularity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_10112 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological singularities arising from fractional-gradient energies Alicandro, Roberto Braides, Andrea Solci, Margherita Stefani, Giorgio Analysis of PDEs Primary 49J45. Secondary 35Q56, 46E35 We prove that, on a planar regular domain, suitably scaled functionals of Ginzburg-Landau type, given by the sum of quadratic fractional Sobolev seminorms and a penalization term vanishing on the unitary sphere, $Γ$-converge to vortex-type energies with respect to the flat convergence of Jacobians. The compactness and the $Γ$-$\liminf$ follow by comparison with standard Ginzburg-Landau functionals depending on Riesz potentials. The $Γ$-$\limsup$, instead, is achieved via a direct argument by joining a finite number of vortex-like functions suitably truncated around the singularity. |
| title | Topological singularities arising from fractional-gradient energies |
| topic | Analysis of PDEs Primary 49J45. Secondary 35Q56, 46E35 |
| url | https://arxiv.org/abs/2309.10112 |