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lions-stampacchia theorem

ESAIM: Control, Optimisation and Calculus of Variations (1)

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A converse to the Lions-Stampacchia Theorem
Emil Ernst, Michel Théra
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 15 / Issue 4 / October 2009

Published online by Cambridge University Press:

20 August 2008, pp. 810-817

Print publication:

October 2009
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In this paper we show that a linear variational inequality over an infinite dimensional real Hilbert spaceadmits solutions for every nonempty bounded closed and convex set, if and only if the linear operator involved in the variational inequality is pseudo-monotone in the sense of Brezis.