Nonlinear weakly elliptic 2X2 systems of variational inequalities with unilateral obstacle constraints

Abstract

We study $2 imes 2$ systems of variational inequalities which are only weakly elliptic; in particular, these systems are not necessarily monotone. The prototype differential operator is the (vector-valued) p-Laplacian. We prove, under certain conditions, the existence of solutions to the unilateral obstacle problem. This work extends the results by the authors in [Annali di Mat. Pura ed Appl., 169(1995), 183--201] to nonlinear operators.

Keywords

• p-Laplacian
• obstacle problem
• non-monotone systems of variational inequalities.