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Inéquations variationnelles fortement non linéaires et applications : [comparaisons des solutions et applications]

Abstract : Comparison results of the solutions for two variational inequalities with the same operateur and two convex sets defined by pointwise constraints are obtained with little restrictive hypotheses. As a corollary, we prove uniqueness results and more genrally monotonicity properties for a large class of variational inequalities associated with convex sets whose pointwise constraints are standard. With these results one can show when the operateur fails to be smooth at zero, some variational inequalities can develop a free boundary. Finally, thaks to our uniqueness theorem, the existence method that we have used allows us to solve numerically a non-linear problem with a transport term
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Gérard Michaille. Inéquations variationnelles fortement non linéaires et applications : [comparaisons des solutions et applications]. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1988. Français. ⟨NNT : 1988METZ002S⟩. ⟨tel-01775745⟩

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