Very weak solutions to the two dimensional Monge-Ampére equation

2019/03/14 by Cao, Wentao, Székelyhidi, László · 2 citations
#35M10 #76B03 #76F02 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.06213

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-Pakzad \citeLewicka:2015gz with a new diagonalization procedure which avoids the use of conformal coordinates, which was introduced by the second author with De Lellis and Inauen in \citeDeLellis:2015wm for the isometric immersion problem.

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• Hyperbolic Monge-Ampère Equation on a Cylinder: Well-Posedness and Stability
• Isometric Immersions and Weak Solutions to the Darboux Equation

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