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Revisiting the $C^{1,\alpha}$ $h$-principle for the Monge–Ampère equation

Jean-Paul Daniel and Peter Hornung

Vol. 15 (2022), No. 7, 1763–1774
Abstract

We provide a simple proof of a C1,α h-principle for the Monge–Ampère equation in two dimensions. Our proof only makes use of the available constructions for isometric immersions and deduces the desired results for the Monge–Ampère equation by exploiting the connections between this equation and the isometric immersion system.

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Keywords
$h$-principle, convex integration, isometric embeddings, Monge–Ampère, von Kármán, nonlinear elasticity
Mathematical Subject Classification
Primary: 35J96, 76B03
Milestones
Received: 9 May 2020
Revised: 7 September 2020
Accepted: 16 March 2021
Published: 5 December 2022
Authors
Jean-Paul Daniel
Fakultät Mathematik
TU Dresden
Dresden
Germany
Peter Hornung
Fakultät Mathematik
TU Dresden
Dresden
Germany