Geodesic
A Garding inequality based unified approach to various classes of semi-coercive variational inequalities applied to non-monotone contact problems with a nested max-min superpotential
Minimax theory and its applications, Tome 5 (2020) no. 1
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We present a unified existence and approximation theory for various classes of variational inequalities (VIs) in reflexive Banach spaces. The focus is on semi-coercive problems. Here we abandon projections, which are limited to a Hilbert space setting, instead we adopt semicoercivity of the elliptic linear operator in form of a Gårding inequality. Also we extend the smoothing procedure from [43] to provide smoothing approximations of nested max-min functions. Then we couple this regularization technique with the finite element method to solve numerically semi-coercive hemivariational inequalities (HVIs) involving a nested max-min superpotential and apply our approximation theory for pseudomonotone VIs to these HVIs. As a model example we consider a unilateral semi-coercive contact problem with non-monotone friction on the contact boundary.
Mots-clés : Hemivariational inequality, pseudomonotonicity, semicoercivity, Gårding inequality, max-min superpotential, smoothing approximation, finite element discretization, non-monotone contact 
@article{MTA_2020_5_1_a7,
     author = {Joachim Gwinner and Nina Ovcharova},
     title = {A {Garding} inequality based unified approach to various classes of semi-coercive variational inequalities applied to non-monotone contact problems with a nested max-min superpotential},
     journal = {Minimax theory and its applications},
     year = {2020},
     volume = {5},
     number = {1},
     zbl = {1437.35366},
     url = {http://geodesic.mathdoc.fr/item/MTA_2020_5_1_a7/}
}
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Joachim Gwinner; Nina Ovcharova. A Garding inequality based unified approach to various classes of semi-coercive variational inequalities applied to non-monotone contact problems with a nested max-min superpotential. Minimax theory and its applications, Tome 5 (2020) no. 1. http://geodesic.mathdoc.fr/item/MTA_2020_5_1_a7/