Global $$C^{1,\alpha }$$ regularity for Monge-Ampère equations on planar convex domains
Abstract In this paper, we establish the global Hölder gradient estimate for solutions to the Dirichlet problem of the Monge-Ampère equation $$\det D^2u = f$$ on strictly convex but not uniformly convex domain $$\Omega$$ .
Authors
- Jiakun Liu (ORCID: https://orcid.org/0000-0003-4409-4187)
- Qing Han (ORCID: https://orcid.org/0000-0003-4585-4678)
- Yang Zhou (ORCID: https://orcid.org/0000-0003-3700-2125)
Institutions
- University of Notre Dame (US)
- The University of Sydney (AU)
- Chinese University of Hong Kong (HK)
Publication Details
- Journal
- Mathematische Annalen
- Published
- 2025-08-25
- DOI
- https://doi.org/10.1007/s00208-025-03250-2
- Primary Topic
- Geometry and complex manifolds
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- University of Sydney