Nonlinear Weakly Elliptic 2X2 Systems of Variational Inequalities with Unilateral Obstacle Constraints
Date
1997-10-31
Authors
Adams, David R.
Nussenzveig Lopes, Helena J.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
p-Laplacian, Obstacle problem, Non-monotone systems of variational inequalities
Citation
Adams, D. R., & Nussenzveig Lopes, H. J. (1997). Nonlinear weakly elliptic 2 x 2 systems of variational inequalities with unilateral obstacle constraints. <i>Electronic Journal of Differential Equations, 1997</i>(18), pp. 1-20.
Rights
Attribution 4.0 International