$C^{1,\alpha }$ $h$-principle for von Kármán 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.