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This is a Quantitative Study study.

September 24, 2025Open Access

C1,α regularity of the solution for the obstacle problem for the linearized Monge-Ampère operator

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Local C^{1,γ} regularity for solutions is established, enhancing understanding of nonlinear PDE behavior.
The primary result proves that a viscosity solution exists and is unique under specific conditions.
Perron's method and the comparison principle are key tools used to analyze the obstacle problem.
This work highlights the advancements in the study of Monge-Ampère operators and the significance of C^{1,γ} regularity.

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Implication

Analysis of viscosity solutions in convex domains reveals local C^{1,γ} regularity, suggesting implications for nonlinear partial differential equations.

Cite This Study

Meng Ji (2025) studied this question.

synapsesocial.com/papers/68d6e16f8b2b6861e4c3ff62 https://doi.org/10.48550/arxiv.2505.24410

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Implication

Analysis of viscosity solutions in convex domains reveals local C^{1,γ} regularity, suggesting implications for nonlinear partial differential equations.

C1,α regularity of the solution for the obstacle problem for the linearized Monge-Ampère operator

Key Points

Discussion

Implication

Cite This Study

C1,α regularity of the solution for the obstacle problem for the linearized Monge-Ampère operator

Key Points

Discussion

Implication

Cite This Study

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