Boundary regularity of Riesz potential, smooth solution to the chord log-Minkowski problem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910563951443968 |
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| author | Hu, Jinrong Huang, Yong Lu, Jian |
| author_facet | Hu, Jinrong Huang, Yong Lu, Jian |
| contents | The Riesz potential and its potential theory are closely related to the regularity of solutions to partial differential equations. In this paper, we investigate a class of Minkowski type problems that are closely associated with convex geometry and geometric probability. This investigation leads to a novel result regarding the boundary regularity of the Riesz potential, which is essential for developing the regularity theory of a new nonlocal {M}onge-{A}mpère equation. As an initial application, the existence of a smooth solution to the chord log-Minkowski problem shall be obtained from the perspective of a nonlocal elliptical partial differential equation and a nonlocal Gauss curvature flow equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14220 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Boundary regularity of Riesz potential, smooth solution to the chord log-Minkowski problem Hu, Jinrong Huang, Yong Lu, Jian Analysis of PDEs The Riesz potential and its potential theory are closely related to the regularity of solutions to partial differential equations. In this paper, we investigate a class of Minkowski type problems that are closely associated with convex geometry and geometric probability. This investigation leads to a novel result regarding the boundary regularity of the Riesz potential, which is essential for developing the regularity theory of a new nonlocal {M}onge-{A}mpère equation. As an initial application, the existence of a smooth solution to the chord log-Minkowski problem shall be obtained from the perspective of a nonlocal elliptical partial differential equation and a nonlocal Gauss curvature flow equation. |
| title | Boundary regularity of Riesz potential, smooth solution to the chord log-Minkowski problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2304.14220 |