Appl Math Optim 51:361–372 (2005)
2005 Springer Science+Business Media, Inc.
Strong Solvability of Boundary Value Contact Problems
D.I.M.E.T., Faculty of Engineering, University of Reggio Calabria,
Via Graziella, Loc. Feo di Vito, Reggio Calabria, Italy
Abstract. Strong solvability in Sobolev spaces is proved for a unilateral con-
tact boundary value problem for a class of nonlinear discontinuous operators. The
operator is assumed to be of Carath´eodory 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.
Key Words. Unilateral contact problems, Nonlinear elliptic equations.
AMS Classiﬁcation. Primary 35J85, Secondary 35R05.
The paper deals with the strong solvability of the following boundary value problem
with unilateral boundary conditions:
− λu = f (x) a.e.in ⊂ R
u ≥ 0,
≥ 0, u ·
where the number λ is greater than zero and χ is the unit outward normal to the boundary
The results of this paper have been presented at the International Conference on “Equilibrium Problems
and Variational Models” and an abridged version of this paper has been published in .