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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.15450 |
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| _version_ | 1866916136000421888 |
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| author | Engl, Dominik Kreisbeck, Carolin Morandotti, Marco |
| author_facet | Engl, Dominik Kreisbeck, Carolin Morandotti, Marco |
| contents | Lower semicontinuity of surface energies in integral form is known to be equivalent to BV-ellipticity of the surface density. In this paper, we prove that BV-ellipticity coincides with the simpler notion of biconvexity for a class of densities that depend only on the jump height and jump normal, and are positively 1-homogeneous in the first argument. The second main result is the analogous statement in the setting of bounded deformations, where we show that BD-ellipticity reduces to symmetric biconvexity. Our techniques are primarily inspired by constructions from the analysis of structured deformations and the general theory of free discontinuity problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizing BV- and BD-ellipticity for a class of positively 1-homogeneous surface energy densities Engl, Dominik Kreisbeck, Carolin Morandotti, Marco Analysis of PDEs Optimization and Control 49J45 (Primary) 26B25, 9Q20, 70G75 (Secondary) Lower semicontinuity of surface energies in integral form is known to be equivalent to BV-ellipticity of the surface density. In this paper, we prove that BV-ellipticity coincides with the simpler notion of biconvexity for a class of densities that depend only on the jump height and jump normal, and are positively 1-homogeneous in the first argument. The second main result is the analogous statement in the setting of bounded deformations, where we show that BD-ellipticity reduces to symmetric biconvexity. Our techniques are primarily inspired by constructions from the analysis of structured deformations and the general theory of free discontinuity problems. |
| title | Characterizing BV- and BD-ellipticity for a class of positively 1-homogeneous surface energy densities |
| topic | Analysis of PDEs Optimization and Control 49J45 (Primary) 26B25, 9Q20, 70G75 (Secondary) |
| url | https://arxiv.org/abs/2402.15450 |