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