Geodesic
Nonlinear weakly elliptic $2\times 2$ systems of variational inequalities with unilateral obstacle constraints
Electronic Journal of Differential Equations, Tome 1997 (1997).

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Summary: We study 2X2 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. In addition, we address the question of determining function spaces on which the p-Laplacian is a bounded nonlinear operator. This question arises naturally when studying existence for these systems.
Classification : 35J85, 35J45, 31C45
Keywords: p-Laplacian, obstacle problem, non-monotone systems of variational inequalities 
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     author = {Adams, D.R. and Nussenzveig Lopes, H.J.},
     title = {Nonlinear weakly elliptic $2\times 2$ systems of variational inequalities with unilateral obstacle constraints},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1997},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a6/}
}
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Adams, D.R.; Nussenzveig Lopes, H.J. Nonlinear weakly elliptic $2\times 2$ systems of variational inequalities with unilateral obstacle constraints. Electronic Journal of Differential Equations, Tome 1997 (1997). http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a6/