Variational inequalities with lack of ellipticity. Part I: Optimal interior regularity and non-degeneracy of the free boundary Donatella DanielliNicola GarofaloSandro Salsa 35J8535H2043A85Obstacle problemFree boundariesSub-elliptic equationsCarnot groupsTheorems of Rademacher-Stepanov type Indiana University Mathematics Journal 2003 text pdf 10.1512/iumj.2003.52.2088 10.1512/iumj.2003.52.2088 en Indiana Univ. Math. J. 52 (2003) 361 - 398 state-of-the-art mathematics http://iumj.org/access/