Revisiting the C1,α h-principle for the Monge–Ampère equation

Daniel, Jean-Paul; Hornung, Peter

doi:10.2140/apde.2022.15.1763

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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

DOI: 10.2140/apde.2022.15.1763

Abstract

We provide a simple proof of a $C^{1, α}$ $h$ -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.

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

Vol. 15, No. 7, 2022