A version of the Lax-Milgram theorem for locally convex spaces. (English) Zbl 1196.46003
An extension of the Lax-Milgram lemma is presented in the setting of locally convex spaces. It is shown that this version of the Lax-Milgram lemma does not admit an analogous generalization for the multilinear case. However, a positive partial result in given.
Reviewer: Qamrul Hasan Ansari (Aligarh)
MSC:
46A03 | General theory of locally convex spaces |
49J40 | Variational inequalities |
58E30 | Variational principles in infinite-dimensional spaces |