Electronic Journal of Differential Equations,
Vol. 1997(1997), No. 18, pp 1-20.
Title: Nonlinear weakly elliptic 2X2 c 2X2 systems of variational
inequalities with unilateral obstacle constraints
Authors: D.R. Adams (Univ. of Kentucky, Lexington, KY, USA)
H.J. Nussenzveig Lopes (IMECC-UNICAMP, Campinas, Brazil)
Abstract:
We study $2 \times 2$ 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., {\bf 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.