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Journal of Convex Analysis 16 (2009), No. 3, 993--1002
Copyright Heldermann Verlag 2009

A Version of the Lax-Milgram Theorem for Locally Convex Spaces

Manuel Ruiz Galán
University of Granada, E. U. Arquitectura Tecnica, Dept. of Applied Mathematics, c/ Severo Ochoa s/n, 18071 Granada, Spain

We show an extension of the Lax-Milgram theorem for the context of locally convex spaces. Furthermore we prove that such version of the Lax-Milgram theorem does not admit an analogous generalization for the multilinear case, even though we give a positive partial result.

Keywords: Lax--Milgram theorem, variational inequalities.

MSC: 58E30, 49J40

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