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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.14659 |
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| _version_ | 1866911856385327104 |
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| author | De Filippis, Cristiana Koch, Lukas Kristensen, Jan |
| author_facet | De Filippis, Cristiana Koch, Lukas Kristensen, Jan |
| contents | We introduce a new quantification of nonuniform ellipticity in variational problems via convex duality, and prove higher differentiability and $2d$-smoothness results for vector valued minimizers of possibly degenerate functionals. Our framework covers convex, anisotropic polynomials as prototypical model examples - in particular, we improve in an essentially optimal fashion Marcellini's original results \cite{ma1}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14659 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantified Legendreness and the regularity of minima De Filippis, Cristiana Koch, Lukas Kristensen, Jan Analysis of PDEs We introduce a new quantification of nonuniform ellipticity in variational problems via convex duality, and prove higher differentiability and $2d$-smoothness results for vector valued minimizers of possibly degenerate functionals. Our framework covers convex, anisotropic polynomials as prototypical model examples - in particular, we improve in an essentially optimal fashion Marcellini's original results \cite{ma1}. |
| title | Quantified Legendreness and the regularity of minima |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2312.14659 |