Global C1,α regularity for Monge-Ampère equations on planar convex domains

Qing Han; Jiakun Liu; Yang Zhou

doi:10.1007/s00208-025-03250-2

August 25, 2025Mathematische AnnalenOpen Access

Global C1,α regularity for Monge-Ampère equations on planar convex domains

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Key Points

Global Hölder gradient estimates were established for solutions to the Monge-Ampère equation.
The research involved Dirichlet problems defined on strictly convex but not uniformly convex domain.
The Monge-Ampère equations serve as a vital tool in differential geometry and optimal transport theory.
This finds relevance in understanding geometric properties of solutions in broader contexts, extending their use.

Implication

Analysis establishes Hölder gradient estimates for Monge-Ampère solutions in strictly convex domains, suggesting broader applicability.

Abstract

In this paper, we establish the global Hölder gradient estimate for solutions to the Dirichlet problem of the Monge-Ampère equation D²u = f on strictly convex but not uniformly convex domain Ω .

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Cite This Study

Han et al. (2025) studied this question.

synapsesocial.com/papers/68af5f0dad7bf08b1eae1c02 https://doi.org/10.1007/s00208-025-03250-2

View Full Paper

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Global C1,α regularity for Monge-Ampère equations on planar convex domains

Key Points

Implication

Abstract

Discussion

Cite This Study

Global C1,α regularity for Monge-Ampère equations on planar convex domains

Key Points

Implication

Abstract

Discussion

Cite This Study

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