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PreprintarXiv licencearXiv

Regularity of Free Boundary for Monge-Ampère Obstacle Problem up to the Boundary

  • Hanfei Han
  • Genggeng Huang
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Abstract

In this paper, we study the regularity of free boundaries for Monge-Ampère obstacle problem up to the boundary. We mainly focus on how the growth order of boundary value near the contact point impact the regularity. We also find an interesting phenomena that under quadratic growth boundary value, the free boundary enjoys better regularity in high dimensions than in two dimension.

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Cite

BibTeXRIS
BibTeX
@misc{han2026regularity,
  title = {{Regularity of Free Boundary for Monge-Ampère Obstacle Problem up to the Boundary}},
  author = {Hanfei Han and Genggeng Huang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08351},
  eprint = {2610.08351},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08351},
}
RIS
TY  - UNPB
TI  - Regularity of Free Boundary for Monge-Ampère Obstacle Problem up to the Boundary
AU  - Hanfei Han
AU  - Genggeng Huang
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08351
UR  - https://arxiv.org/abs/2610.08351
AB  - In this paper, we study the regularity of free boundaries for Monge-Ampère obstacle problem up to the boundary. We mainly focus on how the growth order of boundary value near the contact point impact the regularity. We also find an interesting phenomena that under quadratic growth boundary value, the free boundary enjoys better regularity in high dimensions than in two dimension.
ER  -