Very weak solutions to the two-dimensional Monge-Ampére equation Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday |
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引用本文: | Wentao Cao,László Székelyhidi Jr..Very weak solutions to the two-dimensional Monge-Ampére equation Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday[J].Science China Mathematics,2019(6). |
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作者姓名: | Wentao Cao László Székelyhidi Jr. |
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摘 要: | In this short note we revisit the convex integration approach to constructing very weak solutions to the 2D Monge-Ampére equation with H?lder-continuous ?rst 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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