Abstract
AbstractIn this paper we examine a class of elliptic quasi-variational inequalities, which involve a constraint set and a set-valued map. First, we establish the existence of a solution and the compactness of the solution set. The approach is based on results for an elliptic variational inequality and the Kakutani-Ky Fan fixed point theorem. Next, we prove an existence and compactness result for a quasi-variational-hemivariational inequality. The latter involves a locally Lipschitz continuous functional and a convex potential. Finally, we present an application to the stationary incompressible Navier-Stokes equation with mixed boundary conditions which model a generalized Newtonian fluid of Bingham type.
Funder
H2020 Marie Skłodowska-Curie Actions
Ministerstwo Edukacji i Nauki
Narodowe Centrum Nauki
Publisher
Springer Science and Business Media LLC
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