The Monge-Ampere system in dimension two and codimension three

2025/01/21 by Inauen, Dominik, Lewicka, Marta · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.12474

Abstract

We revisit the convex integration constructions for the Monge-Ampère system and prove its flexibility in dimension d=2 and codimension k=3, up to C^1,1-1/√(5). To our knowledge, it is the first result in which the obtained Hölder exponent 1-(1)/(√(5)) is larger than 1/2 but it is not contained in the full flexibility up to C^1,1 result. Previous various approaches, based on Kuiper's corrugations, always led to the Hölder regularity not exceeding C^1,1/2, while constructions based on the Nash spirals (when applicable) led to the regularity C^1,1. Combining the two approaches towards an interpolation between their corresponding exponent ranges has been so far an open problem.

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