Strong Solvability of Boundary Value Contact Problems

Strong solvability in Sobolev spaces is proved for a unilateral contact boundary value problem for a class of
nonlinear discontinuous operators. The operator is assumed to be of Caratheodory type and to satisfy a suitable ellipticity
condition. Only measurability with respect to the independent variable x is required. The main tool of the proof is an estimate for the second derivatives of the functions which satisfy
the unilateral boundary conditions, in which it has been possible to prove that the constant is equal to 1.