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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/2412.14997 |
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| _version_ | 1866908585347252224 |
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| author | Fußangel, Lukas Priyasad, Buddhika Stephan, Paul |
| author_facet | Fußangel, Lukas Priyasad, Buddhika Stephan, Paul |
| contents | We investigate regularity properties of minimizers for non-autonomous convex variational integrands $F(x, \mathrm{D} u)$ with linear growth, defined on bounded Lipschitz domains $Ω\subset \mathbb{R}^n$. Assuming appropriate ellipticity conditions and Hölder continuity of $\mathrm{D}_zF(x,z)$ with respect to the first variable, we establish higher integrability of the gradient of minimizers and provide bounds on the Hausdorff dimension of the singular set of minimizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14997 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the singular set of $\operatorname{BV}$ minimizers for non-autonomous functionals Fußangel, Lukas Priyasad, Buddhika Stephan, Paul Analysis of PDEs 35B65, 35J47, 49N60 We investigate regularity properties of minimizers for non-autonomous convex variational integrands $F(x, \mathrm{D} u)$ with linear growth, defined on bounded Lipschitz domains $Ω\subset \mathbb{R}^n$. Assuming appropriate ellipticity conditions and Hölder continuity of $\mathrm{D}_zF(x,z)$ with respect to the first variable, we establish higher integrability of the gradient of minimizers and provide bounds on the Hausdorff dimension of the singular set of minimizers. |
| title | On the singular set of $\operatorname{BV}$ minimizers for non-autonomous functionals |
| topic | Analysis of PDEs 35B65, 35J47, 49N60 |
| url | https://arxiv.org/abs/2412.14997 |