Partial regularity for variational integrals with Morrey-Hölder zero-order terms, and the limit exponent in Massari's regularity theorem
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914373535006720 |
|---|---|
| author | Schmidt, Thomas Schütt, Jule Helena |
| author_facet | Schmidt, Thomas Schütt, Jule Helena |
| contents | We revisit the partial $\mathrm{C}^{1,α}$ regularity theory for minimizers of non-parametric integrals with emphasis on sharp dependence of the Hölder exponent $α$ on structural assumptions for general zero-order terms. A particular case of our conclusions carries over to the parametric setting of Massari's regularity theorem for prescribed-mean-curvature hypersurfaces and there confirms optimal regularity up to the limit exponent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03338 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial regularity for variational integrals with Morrey-Hölder zero-order terms, and the limit exponent in Massari's regularity theorem Schmidt, Thomas Schütt, Jule Helena Analysis of PDEs 49N60, 35B65 (primary), 49Q05, 53A10, 35J47, 35J93 (secondary) We revisit the partial $\mathrm{C}^{1,α}$ regularity theory for minimizers of non-parametric integrals with emphasis on sharp dependence of the Hölder exponent $α$ on structural assumptions for general zero-order terms. A particular case of our conclusions carries over to the parametric setting of Massari's regularity theorem for prescribed-mean-curvature hypersurfaces and there confirms optimal regularity up to the limit exponent. |
| title | Partial regularity for variational integrals with Morrey-Hölder zero-order terms, and the limit exponent in Massari's regularity theorem |
| topic | Analysis of PDEs 49N60, 35B65 (primary), 49Q05, 53A10, 35J47, 35J93 (secondary) |
| url | https://arxiv.org/abs/2410.03338 |