Local and global minimality of the lamella for the anisotropic Ohta-Kawasaki energy
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913034829561856 |
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| author | Fiorini, Alberto |
| author_facet | Fiorini, Alberto |
| contents | In this paper we consider the volume-constrained minimization of a variant of the Ohta-Kawasaki functional with an anisotropic surface energy replacing the standard perimeter. Following and suitably adapting the second variation approach devised in arXiv:1211.0164, we prove local minimality results for the horizontal lamellar configuration, in analogy with the isotropic case, under the assumption that the anisotropy is uniformly elliptic. If instead the Wulff shape of the anisotropy has upper and lower horizontal facets, we prove that the lamella exhibits a rigid behavior and is an isolated local minimizer for all parameter values. We conclude by showing some global minimality results, mostly focusing on the planar case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_13736 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local and global minimality of the lamella for the anisotropic Ohta-Kawasaki energy Fiorini, Alberto Analysis of PDEs 49Q10 (Primary), 49Q20 (Secondary) In this paper we consider the volume-constrained minimization of a variant of the Ohta-Kawasaki functional with an anisotropic surface energy replacing the standard perimeter. Following and suitably adapting the second variation approach devised in arXiv:1211.0164, we prove local minimality results for the horizontal lamellar configuration, in analogy with the isotropic case, under the assumption that the anisotropy is uniformly elliptic. If instead the Wulff shape of the anisotropy has upper and lower horizontal facets, we prove that the lamella exhibits a rigid behavior and is an isolated local minimizer for all parameter values. We conclude by showing some global minimality results, mostly focusing on the planar case. |
| title | Local and global minimality of the lamella for the anisotropic Ohta-Kawasaki energy |
| topic | Analysis of PDEs 49Q10 (Primary), 49Q20 (Secondary) |
| url | https://arxiv.org/abs/2604.13736 |