Direct minimization of the Canham--Helfrich energy on generalized Gauss graphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910287216508928 |
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| author | Kubin, Anna Lussardi, Luca Morandotti, Marco |
| author_facet | Kubin, Anna Lussardi, Luca Morandotti, Marco |
| contents | The existence of minimizers of the Canham--Helfrich functional in the setting of generalized Gauss graphs is proved. As a first step, the Canham--Helfrich functional, usually defined on regular surfaces, is extended to generalized Gauss graphs, then lower semicontinuity and compactness are proved under a suitable condition on the bending constants ensuring coerciveness; the minimization follows by the direct methods of the Calculus of Variations. Remarks on the regularity of minimizers and on the behavior of the functional in case there is lack of coerciveness are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_06353 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Direct minimization of the Canham--Helfrich energy on generalized Gauss graphs Kubin, Anna Lussardi, Luca Morandotti, Marco Optimization and Control 49Q20 The existence of minimizers of the Canham--Helfrich functional in the setting of generalized Gauss graphs is proved. As a first step, the Canham--Helfrich functional, usually defined on regular surfaces, is extended to generalized Gauss graphs, then lower semicontinuity and compactness are proved under a suitable condition on the bending constants ensuring coerciveness; the minimization follows by the direct methods of the Calculus of Variations. Remarks on the regularity of minimizers and on the behavior of the functional in case there is lack of coerciveness are presented. |
| title | Direct minimization of the Canham--Helfrich energy on generalized Gauss graphs |
| topic | Optimization and Control 49Q20 |
| url | https://arxiv.org/abs/2201.06353 |