Electron. J. Diff. Eqns., Vol. 1997(1997), No. 18, pp 1-20.

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

D.R. Adams & H.J. Nussenzveig Lopes

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.

Submitted July 28, 1997. Published October 31, 1997.
Math Subject Classification: 35J85, 35J45, 31C45.
Key Words: p-Laplacian, obstacle problem, non-monotone systems of variational inequalities.

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David R. Adams
Department of Mathematics, University of Kentucky, Patterson Office Tower, Lexington, KY 40506, USA
e-mail: dave@ms.uky.edu

Helena J. Nussenzveig Lopes
Departamento de Matematica, IMECC-UNICAMP. Caixa Postal 6065, Campinas, SP 13081-970, Brazil
e-mail: hlopes@ime.unicamp.br

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