Geodesic
Nonlinear weakly elliptic \(2\times 2\) systems of variational inequalities with unilateral obstacle constraints
Electronic journal of differential equations, Tome 1997 (1997)
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 
@article{EJDE_1997__1997__a30,
     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},
     year = {1997},
     volume = {1997},
     zbl = {0890.35056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a30/}
}
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%J Electronic journal of differential equations
%D 1997
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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__a30/