Sufficient conditions for an existence of a solution to a differential inclusion (Q2922471)

The author ``formulate[s] geometric conditions induced by the compact set \(K\subset \mathbb{R}^{m\times n}\) which imply the existence of a Lipschitz solution \(u\) to the differential inclusion \(Du\in K\). The solutions are obtained using the convex integration method.'' The author illustrates the ''result for the known example \(K=SO(2)\cup SO(2)B,\) where \(B\) is a \(2\times 2\) diagonal matrix with \(\text{det}B=1\).'' (from author's abstract)