Enclosure results for quasilinear systems of variational inequalities |
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Authors: | S Carl |
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Institution: | a Fachbereich Mathematik und Informatik, Institut für Analysis, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle, Germany b Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, MO 65401, USA |
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Abstract: | 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. |
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Keywords: | System of variational inequalities Leray-Lions operator Sub-supersolution Enclosure Extremal solution |
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