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

Published online by Cambridge University Press:  17 February 2009

Vy Khoi Le
Vy Khoi Le
Affiliation:
Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, MO 65409, USA; e-mail: [email protected].
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Abstract

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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.

Keywords

sub-supersolutionsandpile problemvariational inequalityextremal solution.
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 2 , October 2006 , pp. 179 - 197
Copyright
Copyright © Australian Mathematical Society 2006

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