Abstract quasi-variational inequalities of elliptic type and applications

Tom 86 / 2009

Yusuke Murase Banach Center Publications 86 (2009), 235-246 MSC: Primary 35K45; Secondary 35K50. DOI: 10.4064/bc86-0-15


A class of quasi-variational inequalities (QVI) of elliptic type is studied in reflexive Banach spaces. The concept of QVI was earlier introduced by A. Bensoussan and J.-L. Lions [2] and its general theory has been developed by many mathematicians, for instance, see [6, 7, 9, 13] and a monograph [1]. In this paper we give a generalization of the existence theorem established in [14]. In our treatment we employ the compactness method along with a concept of convergence of nonlinear multivalued operators of monotone type (cf. [11]). We shall prove an abstract existence result for our class of QVI's, and moreover, give some applications to QVI's for elliptic partial differential operators.


  • Yusuke MuraseFaculty of Economic Sciences
    Hiroshima Shudo University
    1-1-1 Ozuka-higashi, Asaminami-Ku
    Hiroshima, 731-3195, Japan

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