Enclosure Results for Quasilinear Systems of Variational Inequalities
In this paper we consider systems of quasilinear elliptic variational inequalities, and prove the existence of minimal and maximal (in the set theoretical sense) solutions within some ordered interval of an appropriately defined pair of sub- and supersolutions. We show that the notion of sub- and supersolutions of variational inequalities introduced here is consistent with the usual notion of sub-supersolutions for (variational) equations. For weakly coupled quasimonotone systems of variational inequalities the existence of smallest and greatest solutions is proved.
V. K. Le and S. Carl, "Enclosure Results for Quasilinear Systems of Variational Inequalities," Journal of Differential Equations, Elsevier, May 2004.
The definitive version is available at https://doi.org/10.1016/j.jde.2003.10.009
Mathematics and Statistics
Keywords and Phrases
Leray-Lions operator; enclosure; external solution; sub-supersolution; system of variational inequalities
Article - Journal
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