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Journal of Convex Analysis 28 (2021), No. 1, 237--250
Copyright Heldermann Verlag 2021

Existence of a Solution to a Stationary Quasi-Variational Inequality in a Multi-Connected Domain

Junichi Aramaki
Division of Science, Faculty of Science and Engineering, Tokyo Denki University, Saitama 350-0394, Japan

We consider a stationary quasi-variational inequality in a multi-connected domain and show the existence of a solution to the inequality. The problem is related to the Bean critical-state model in type II superconductors. Mathematically, we are concerned with a quasi-variational inequality containing a p-curl inequality with a curl constraint by a function of the solution.

Keywords: Quasi-variational inequality, stationary variational problem, existence of solution.

MSC: 35A15, 35J20, 35H30, 35D05, 35Q60.

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