ANZIAM  J.  48 (2006), 179-197

Sub-supersolutions in a variational inequality related to a sandpile problem

Vy Khoi Le   Department of Mathematics and Statistics   University of Missouri-Rolla   Rolla   MO 65409   USA     vy@umr.edu

Abstract

In this paper we study a variational inequality in which the principal operator is a generalised Laplacian with fast growth at infinity and slow growth at 0. By defining appropriate sub- and super-solutions, we show the existence of solutions and extremal solutions of this inequality above the subsolutions or between the sub- and super-solutions.

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