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arXiv · 2311.17291

Regularity for the Monge-Amp\`ere equation by doubling

Ravi Shankar·Yu Yuan
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Abstract

We give a new proof for the interior regularity of strictly convex solutions of the Monge-Amp\`ere equation. Our approach uses a doubling inequality for the Hessian in terms of the extrinsic distance function on the maximal Lagrangian submanifold determined by the potential equation.

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Ravi Shankar, Yu Yuan. 2023-11-29. Regularity for the Monge-Amp\`ere equation by doubling. https://arxiv.org/abs/2311.17291

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