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Mathematics in Engineering

2023, Volume 5, Issue 2: 1-6. doi: 10.3934/mine.2023037
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A monotonicity approach to Pogorelov's Hessian estimates for Monge- Ampère equation

  • Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195, USA
  • Received: 21 April 2022 Revised: 25 May 2022 Accepted: 25 May 2022 Published: 02 June 2022

  • We present an integral approach to Pogorelov's Hessian estimates for the Monge-Ampère equation, originally obtained via a pointwise argument.

    Citation: Yu Yuan. A monotonicity approach to Pogorelov's Hessian estimates for Monge- Ampère equation[J]. Mathematics in Engineering, 2023, 5(2): 1-6. doi: 10.3934/mine.2023037

    Related Papers:

  • We present an integral approach to Pogorelov's Hessian estimates for the Monge-Ampère equation, originally obtained via a pointwise argument.


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    [1] L. A. Caffarelli, A priori estimates and the geometry of the Monge Ampère equation, In: Nonlinear partial differential equations in differential geometry, Providence, RI: Amer. Math. Soc., 1996, 5–63.
    [2] D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of second order, Berlin, Heidelberg: Springer, 2001. https://doi.org/10.1007/978-3-642-61798-0
    [3] A. V. Pogorelov, The Minkowski multidimensional problem, New York-Toronto-London: Halsted Press [John Wiley & Sons], 1978.
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