Nonsmooth and nonenergetic solutions of PDE’s through convex integration

In this Master thesis we explore the convex integration method by S. Müller and V. Šverák and its applications to partial differential equations. In particular, we use it to build very irregular solutions to elliptic systems. We also apply this method to build very weak solutions to elliptic scalar-valued partial differential equations. For this, we also use staircase laminates invented by D. Faraco.