Abstract
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.
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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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Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday
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Cao, W., Székelyhidi, L. Very weak solutions to the two-dimensional Monge-Ampére equation. Sci. China Math. 62, 1041–1056 (2019). https://doi.org/10.1007/s11425-018-9516-7
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DOI: https://doi.org/10.1007/s11425-018-9516-7