Strong solvability of boundary value contact problems (Q2506161)

The paper deals with the strong solvability for a unilateral contact boundary value problem for a class of nonlinear discontinuous operators. The problem represents the conceptual model (Signorini problem) of an elastic body \(\Omega\) with boundary \(\partial \Omega\) which is in contact with a rigid support body and is subject to a volume force.The operator of the problem is assumed to be of Carathéodory type and satisfy a suitable ellipticity condition. Related results can be found in [\textit{S. Campanato}, Ann. Mat. Pura Appl. (4) 167, 243--256 (1994; Zbl 0820.47050)]. Only measurability with respect to the independent variable \(x\) is required. The main purpose of this paper is to prove \(W^{2,2}(\Omega)\)-solvability of this problem.