# $C^{1,\alpha}$ $h$-principle for von K\'arm\'an constraints

## TL;DR

This paper establishes a $C^{1,eta}$ convex integration method for a specific nonlinear PDE system related to von Kármán constraints, leveraging connections to isometric immersion problems in two dimensions.

## Contribution

It introduces a new convex integration approach for the von Kármán system by linking it to isometric immersion theory, providing a simplified construction method.

## Key findings

- Constructs $C^{1,eta}$ solutions for the von Kármán system.
- Connects the PDE system to isometric immersion problems.
- Simplifies the convex integration process for these constraints.

## Abstract

Exploiting some connections between the system $\nabla v\otimes\nabla v + 2$ sym $\nabla w = A$ and the isometric immersion problem in two dimensions, we provide a simple construction of $C^{1,\alpha}$ convex integration solutions for the former from the corresponding result for the latter.