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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.09052 |
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| _version_ | 1866929357656686592 |
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| author | Hirsch, Jonas Spolaor, Luca |
| author_facet | Hirsch, Jonas Spolaor, Luca |
| contents | We prove that $2$-dimensional $Q$-valued maps that are stationary with respect to outer and inner variations of the Dirichlet energy are Hölder continuous and that the dimension of their singular set is at most one. In the course of the proof we establish a strong concentration-compactness theorem for equicontinuous maps that are stationary with respect to outer variations only, and which holds in every dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_09052 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Interior regularity for two-dimensional stationary $Q$-valued maps Hirsch, Jonas Spolaor, Luca Analysis of PDEs Differential Geometry 49Q20, 35J99 We prove that $2$-dimensional $Q$-valued maps that are stationary with respect to outer and inner variations of the Dirichlet energy are Hölder continuous and that the dimension of their singular set is at most one. In the course of the proof we establish a strong concentration-compactness theorem for equicontinuous maps that are stationary with respect to outer variations only, and which holds in every dimensions. |
| title | Interior regularity for two-dimensional stationary $Q$-valued maps |
| topic | Analysis of PDEs Differential Geometry 49Q20, 35J99 |
| url | https://arxiv.org/abs/2211.09052 |