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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2111.14740 |
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| _version_ | 1866910796428083200 |
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| author | Irving, Christopher |
| author_facet | Irving, Christopher |
| contents | A partial regularity theorem is presented for minimisers of $k$th-order functionals subject to a quasiconvexity and general growth condition. We will assume a natural growth condition governed by an $N$-function satisfying the $Δ_2$ and $\nabla_2$ conditions, assuming no quantitative estimates on the second derivative of the integrand; this is new even in the $k = 1$ case. These results will also be extended to the case of strong local minimisers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_14740 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Partial regularity for minima of higher-order quasiconvex integrands with natural Orlicz growth Irving, Christopher Analysis of PDEs 35J48, 35J50 A partial regularity theorem is presented for minimisers of $k$th-order functionals subject to a quasiconvexity and general growth condition. We will assume a natural growth condition governed by an $N$-function satisfying the $Δ_2$ and $\nabla_2$ conditions, assuming no quantitative estimates on the second derivative of the integrand; this is new even in the $k = 1$ case. These results will also be extended to the case of strong local minimisers. |
| title | Partial regularity for minima of higher-order quasiconvex integrands with natural Orlicz growth |
| topic | Analysis of PDEs 35J48, 35J50 |
| url | https://arxiv.org/abs/2111.14740 |