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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.15621 |
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Table of Contents:
- In this paper, we establish local and global regularity estimates for linearized Monge-Ampère equations in divergence form via critical Lorentz space estimates for the Green's function of the linearized Monge-Ampère operator and its gradient. These estimates hold under suitable conditions on the data and the convex Monge-Ampère potential is assumed to have Hessian determinant bounded between two positive constants. As an application, we obtain the solvability in all dimensions of the second boundary value problem for a class of singular fourth-order Abreu type equations that arise from the approximation analysis of variational problems subject to convexity constraints.