Convex integration for the Monge-Amp\`ere equation in two dimensions

This paper concerns the questions of flexibility and rigidity of solutions to the Monge-Amp\`ere equation which arises as a natural geometrical constraint in prestrained nonlinear elasticity. In particular, we focus on anomalous i.e. "flexible" weak solutions that can be constructed through methods of convex integration \`a la Nash & Kuiper and establish the related h-principle for the Monge-Amp\`ere equation in two dimensions