Variational, Hemivariational and Variational-Hemivariational Inequalities: Existence Results
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 67)
The celebrated Hartman-Stampacchia theorem (see , Lemma 3.1, or , Theorem I.3.1) asserts that if V is a finite dimensional Banach space, K ⊂ V is non-empty, compact and convex, A : K → V* is continuous, then there exists u ∈ K such that, for every v ∈ K,
$$\langle Au,v - u\rangle \geqslant 0.$$
KeywordsBanach Space Convex Subset Inequality Problem Nonempty Closed Convex Subset Lower Semicontinuous Function
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