A priori $L^\infty-$bound for Ginzburg-Landau energy minimizers with divergence penalization
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917614532427776 |
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| author | Bronsard, Lia Colinet, Andrew Stantejsky, Dominik |
| author_facet | Bronsard, Lia Colinet, Andrew Stantejsky, Dominik |
| contents | We consider minimizers $u_\varepsilon$ of the Ginzburg-Landau energy with quadratic divergence penalization on a simply-connected two-dimensional domain $Ω$. On the boundary, strong tangential anchoring is imposed. We prove that minimizers satisfy a $L^\infty$-bound uniform in $\varepsilon$ when $Ω$ has $C^{2,1}-$boundary and that the Lipschitz constant blows up like $\varepsilon^{-1}$ when $Ω$ has $C^{3,1}-$boundary. Our theorem extends to $W^{2,p}-$regularity result for our elliptic system with mixed Dirichlet-Neumann boundary condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09949 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A priori $L^\infty-$bound for Ginzburg-Landau energy minimizers with divergence penalization Bronsard, Lia Colinet, Andrew Stantejsky, Dominik Analysis of PDEs We consider minimizers $u_\varepsilon$ of the Ginzburg-Landau energy with quadratic divergence penalization on a simply-connected two-dimensional domain $Ω$. On the boundary, strong tangential anchoring is imposed. We prove that minimizers satisfy a $L^\infty$-bound uniform in $\varepsilon$ when $Ω$ has $C^{2,1}-$boundary and that the Lipschitz constant blows up like $\varepsilon^{-1}$ when $Ω$ has $C^{3,1}-$boundary. Our theorem extends to $W^{2,p}-$regularity result for our elliptic system with mixed Dirichlet-Neumann boundary condition. |
| title | A priori $L^\infty-$bound for Ginzburg-Landau energy minimizers with divergence penalization |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.09949 |