Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print) Author Index To Appear Other MSP Journals
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 ${C}^{1,\alpha }$ $h$-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