Work

Solutions to Monge-Ampère Equations with Low Codimensional singularities

Year: 2026

Type: preprint

Abstract: We construct solutions to Monge-Ampère equations whose Monge-Ampère measures contain singular components supported on low codimensional sets. We also study the regularity of such solutions. To motivate our construction, we present examples arising from optimal transport where the potential of optimal transport maps satisfy Monge-Ampère equations similar to the ones we study.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2605.19142

Authors: Rakshit, Arghya, Sen, Aranya

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: CAREER: Singular and Global Solutions to Nonlinear Elliptic Equations

OpenAlex ID: W7161829913

Cites: 3

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Related to: 10