  The thin obstacle problem or $n$-dimensional Signorini problem is a classical
variational problem arising in several applications, starting with its first
introduction in elasticity theory. The vast literature concerns mostly
quadratic energies, whereas only partial results have been proved in the
nonlinear case. In this paper we consider the thin boundary obstacle problem
for a general class of nonlineraities and we prove the optimal $C^{1,
\frac{1}{2}}$-regularity of the solutions in any space dimension.
