Solutions to Monge-Amp\`ere Equations with Low Codimensional singularities
Analysis of PDEs
2026-05-20 v1
Abstract
We construct solutions to Monge-Amp\`ere equations whose Monge-Amp\`ere 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-Amp\`ere equations similar to the ones we study.
Cite
@article{arxiv.2605.19142,
title = {Solutions to Monge-Amp\`ere Equations with Low Codimensional singularities},
author = {Arghya Rakshit and Aranya Sen},
journal= {arXiv preprint arXiv:2605.19142},
year = {2026}
}
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