On the singular set of the free boundary for a Monge-Ampère obstacle problem
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908402014224384 |
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| author | Jin, Tianling Tu, Xushan Xiong, Jingang |
| author_facet | Jin, Tianling Tu, Xushan Xiong, Jingang |
| contents | This is a continuation of our earlier work [14] on the Monge-Ampère obstacle problem \[ \det D^2 v = v^q χ_{\{v>0\}}, \quad v \geq 0 \text{ convex} \] with $q \in [0,n)$, where we studied the regularity of the strictly convex part of the free boundary.
In this work, we examine the non-strictly convex part of the free boundary and establish optimal dimension bounds for its flat portion. Additionally, we investigate the strong maximum principle and a stability property for this Monge-Ampère obstacle problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08387 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the singular set of the free boundary for a Monge-Ampère obstacle problem Jin, Tianling Tu, Xushan Xiong, Jingang Analysis of PDEs This is a continuation of our earlier work [14] on the Monge-Ampère obstacle problem \[ \det D^2 v = v^q χ_{\{v>0\}}, \quad v \geq 0 \text{ convex} \] with $q \in [0,n)$, where we studied the regularity of the strictly convex part of the free boundary. In this work, we examine the non-strictly convex part of the free boundary and establish optimal dimension bounds for its flat portion. Additionally, we investigate the strong maximum principle and a stability property for this Monge-Ampère obstacle problem. |
| title | On the singular set of the free boundary for a Monge-Ampère obstacle problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.08387 |