Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Manuel Ruiz Galán

University of Granada, E. U. Arquitectura Técnica, Dept. of Applied Mathematics, c/ Severo Ochoa s/n, 18071 Granada, Spain

mruizg@ugr.es

Keywords

  • Lax–Milgram theorem
  • variational inequalities

Mathematics Subject Classification

58E30, 49J40

Suggested citation

M. Ruiz Galán. “A Version of the Lax-Milgram Theorem for Locally Convex Spaces.” Journal of Convex Analysis 16 (2009), No. 3&4, 993–1002. https://doi.org/10.68381/jca16061

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Published by Heldermann Verlag, 2009. Rights now held by Banach Press.