A priori estimates and $η-$compactness for anisotropic Ginzburg-Landau minimizers with tangential anchoring
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917065883910144 |
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| author | Bronsard, Lia Colinet, Andrew Stantejsky, Dominik van Brussel, Lee |
| author_facet | Bronsard, Lia Colinet, Andrew Stantejsky, Dominik van Brussel, Lee |
| contents | We consider minimizers $u_\varepsilon$ of the Ginzburg-Landau energy with quadratic divergence or curl penalization on a simply-connected two-dimensional domain $Ω$. On the boundary, strong tangential anchoring is imposed. We prove a priori estimates for $u_\varepsilon$ in $L^\infty$ uniform in $\varepsilon$ and that the Lipschitz constant of $u_\varepsilon$ blows up like $\varepsilon^{-1}$. We then deduce compactness for a subsequence that converges to an $\mathbb{S}^1-$valued map with either one interior point defect or two boundary half-defects. We conclude our study with a proof that no boundary vortices can occur in the divergence penalized case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04672 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A priori estimates and $η-$compactness for anisotropic Ginzburg-Landau minimizers with tangential anchoring Bronsard, Lia Colinet, Andrew Stantejsky, Dominik van Brussel, Lee Analysis of PDEs Classical Analysis and ODEs 49K20, 35B45, 35B38, 35E20, 49S05 We consider minimizers $u_\varepsilon$ of the Ginzburg-Landau energy with quadratic divergence or curl penalization on a simply-connected two-dimensional domain $Ω$. On the boundary, strong tangential anchoring is imposed. We prove a priori estimates for $u_\varepsilon$ in $L^\infty$ uniform in $\varepsilon$ and that the Lipschitz constant of $u_\varepsilon$ blows up like $\varepsilon^{-1}$. We then deduce compactness for a subsequence that converges to an $\mathbb{S}^1-$valued map with either one interior point defect or two boundary half-defects. We conclude our study with a proof that no boundary vortices can occur in the divergence penalized case. |
| title | A priori estimates and $η-$compactness for anisotropic Ginzburg-Landau minimizers with tangential anchoring |
| topic | Analysis of PDEs Classical Analysis and ODEs 49K20, 35B45, 35B38, 35E20, 49S05 |
| url | https://arxiv.org/abs/2511.04672 |