Abstract
The paper proves the existence and uniqueness of the solution for the following multivalued deterministic variational inequality with oblique subgradients, considered in a non-convex domain: {x′(t)+H(t,x(t))∂−φ(x(t))∋g(t,x(t)),t≥0,x(0)=x0, where ∂−φ stands for the Fréchet subdifferential of the semiconvex function φ and the matrix application x↦H(⋅,x) is a Lipschitz mapping. The presence of the oblique reflection brought by the term H∂−φ leads to the use of different techniques comparing to the cases of standard reflection in non-convex domains or oblique reflection in convex domains. The last section of the article is focused on the qualitative analysis of a non-convex Skorohod problem, with generalized reflection and, as applications, stochastic variational inequalities driven by oblique Fréchet subgradients are addressed.
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