2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70199We study Lispchitz solutions of partial differential relations $\nabla u\in K$, where $u$ is a vector-valued function in an open subset of $R^n$. In some cases the set of solutions turns out to be surprisingly large. The general theory is then used to construct counter-examples to regularity of solutions of Euler-Lagrange systems satisfying classical ellipticity conditions.28 pages published versionClassical Analysis and ODEstext