Science China Mathematics

, Volume 62, Issue 6, pp 1041–1056 | Cite as

Very weak solutions to the two-dimensional Monge-Ampére equation

  • Wentao Cao
  • László SzékelyhidiJr.Email author


In this short note we revisit the convex integration approach to constructing very weak solutions to the 2D Monge-Ampére equation with Hölder-continuous first derivatives of exponent β < 1/5. Our approach is based on combining the approach of Lewicka and Pakzad (2017) with a new diagonalization procedure which avoids the use of conformal coordinates, which was introduced by De Lellis et al. (2018) for the isometric immersion problem.


Monge-Ampére equation convex integration weak solutions 


35M10 76B03 76F02 


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The authors thank the hospitality of the Max-Planck Institute for Mathematics in the Sciences, and gratefully acknowledge the support of the European Research Council Grant Agreement (Grant No. 724298).


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© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institut für MathematikUniversität LeipzigLeipzigGermany

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