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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.11279 |
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| _version_ | 1866914309623250944 |
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| author | Ficola, Eleonora Schmidt, Thomas |
| author_facet | Ficola, Eleonora Schmidt, Thomas |
| contents | We develop a semicontinuity-based existence theory in $\mathrm{BV}$ for a general class of scalar linear-growth variational integrals with additional signed-measure terms. The results extend and refine previous considerations for anisotropic total variations and area-type cases, and they pave the way for a variational approach to the corresponding Euler-Lagrange equations, which involve the signed measure as right-hand-side datum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11279 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence theory for linear-growth variational integrals with signed measure data Ficola, Eleonora Schmidt, Thomas Analysis of PDEs 49J45, 35R06, 35J20, 26B30 We develop a semicontinuity-based existence theory in $\mathrm{BV}$ for a general class of scalar linear-growth variational integrals with additional signed-measure terms. The results extend and refine previous considerations for anisotropic total variations and area-type cases, and they pave the way for a variational approach to the corresponding Euler-Lagrange equations, which involve the signed measure as right-hand-side datum. |
| title | Existence theory for linear-growth variational integrals with signed measure data |
| topic | Analysis of PDEs 49J45, 35R06, 35J20, 26B30 |
| url | https://arxiv.org/abs/2505.11279 |