| Issue |
ESAIM: COCV
Volume 15, Number 4, October-December 2009
|
|
|---|---|---|
| Page(s) | 810 - 817 | |
| DOI | https://doi.org/10.1051/cocv:2008054 | |
| Published online | 20 August 2008 | |
A converse to the Lions-Stampacchia Theorem
1
Aix-Marseille Univ, UMR6632, Marseille, 13397, France. Emil.Ernst@univ-cezanne.fr
2
XLIM (UMR-CNRS ) and Université de Limoges, 123 Avenue A. Thomas, 87060
Limoges Cedex, France. michel.thera@unilim.fr
Received:
27
September
2007
Revised:
14
February
2008
In this paper we show that a linear variational inequality over an infinite dimensional real Hilbert space admits 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.
Mathematics Subject Classification: 47H05 / 52A41 / 39B82
Key words: Lions-Stampacchia Theorem / variational inequality / pseudo-monotone operator
© EDP Sciences, SMAI, 2008
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.