Very weak solutions to the two-dimensional Monge-Ampére equation
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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 conformai coordinates, which was introduced by De Lellis et al. (2018) for the isometric immersion problem.
KeywordsMonge-Ampére equation convex integration weak solutions
MSC(2010)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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