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Regularity for the Monge–Ampère equation by doubling

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Abstract

We give a new proof for the interior regularity of strictly convex solutions of the Monge–Ampère 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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Acknowledgements

Y.Y. is partially supported by an NSF grant.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, NJ, 08544-1000, USA

    Ravi Shankar

  2. Department of Mathematics, University of Washington, BOX 354350, Seattle, WA, 98195, USA

    Yu Yuan

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  1. Ravi Shankar
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  2. Yu Yuan
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Correspondence to Ravi Shankar.

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Shankar, R., Yuan, Y. Regularity for the Monge–Ampère equation by doubling. Math. Z. 307, 34 (2024). https://doi.org/10.1007/s00209-024-03508-6

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  • DOI: https://doi.org/10.1007/s00209-024-03508-6

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