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Some new estimates for solutions of degenerate two dimensional Monge-Ampère equations

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Abstract.

We derive a monotonicity formula for smooth solutions u of degenerate two dimensional Monge-Ampère equations, and use this to obtain a local Hölder gradient estimate, depending on ||Δu|| L P for some p > 1.

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Authors and Affiliations

  1. Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia (e-mail: John.Urbas@maths.anu.edu.au) , Australia

    John Urbas

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  1. John Urbas
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Received August 9, 1999; in final form December 8, 1999/ Published online December 8, 2000

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Urbas, J. Some new estimates for solutions of degenerate two dimensional Monge-Ampère equations. Math Z 236, 625–641 (2001). https://doi.org/10.1007/PL00004845

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  • DOI: https://doi.org/10.1007/PL00004845

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