Talk:Weak formulation

Notation

What does "[Au](v) = f(v)" mean?. Please, provide relevant definitions. Sirix 12:55, 9 February 2007 (UTC)[reply]

Well, f(v) is f applied to v, and [Au](v) is in the same way Au applied to v. That's because Au takes values in the dual, so Au is a function. I did not write this stuff, but I don't know how to explain it better. Oleg Alexandrov (talk) 16:14, 9 February 2007 (UTC)[reply]

It should state somewhere that V' is the dual of V. The usual notation is V*. I'm going to go ahead and insert this. Compsonheir (talk) 21:18, 11 April 2009 (UTC)[reply]

Lax–Milgram theorem?

Hi! I noticed the link to the articles in other languages are to Lax–Milgram theorem. Is this correct? In the Italian wikipedia there is an article 'Formulazione debole', which is the exact translation of 'Weak formulation'. Is Lax–Milgram theorem the same as 'Weak formulation'? Correct in case I'm wrong guys. Thanks! --Luca (talk) 15:53, 12 December 2007 (UTC)[reply]

The Lax-Migram theorem is not the same as 'Weak formulation'. However, this 'Weak formulation' does describe the Lax-Milgram theorem, and the link to Lax–Milgram theorem points back here. Therefore, things are OK. Idially somebody would write the Lax–Milgram theorem article, but until then we are stuck with what we have. Oleg Alexandrov (talk) 05:40, 13 December 2007 (UTC)[reply]

Ok. Where should 'Formulazione debole' (italian for 'Weak formulation') point to? Now it points to 'Weak formulation', is this ok? Thanks! --Luca (talk) 13:06, 13 December 2007 (UTC)[reply]

I think it's okay as it is now. Both it:Formulazione debole and it:Lemma di Lax-Milgram point to en:Weak formulation, and en:Weak formulation points to it:Formulazione debole, so every article points to its closest equivalent. -- Jitse Niesen (talk) 15:15, 13 December 2007 (UTC)[reply]

I added a merge template, there is the page Lions–Lax–Milgram theorem which contains about the same stuff, I think all content about Lax-Milgram theorem should be moved to its page rather than having a page in common with Weak formulation. Agi 90 (talk) 15:52, 28 March 2012 (UTC)[reply]

Wouldn't it be better to have a single article on Weak solution theory with subsections on weak solutions, weak formulation, weak derivative, Lax-Milgram theorem, Babuška–Lax–Milgram theorem and Lions-Lax-Milgram theorem? Cesiumfrog (talk) 08:28, 2 January 2016 (UTC)[reply]

As an amateur mathematician, I find the page tricky enough to digest as it is without merging more content in to a combined page. There I oppose the merge proposal. Klbrain (talk) 16:40, 13 May 2016 (UTC)[reply]

Terminology motivation

Why is this formulation termed "weak" (and the usual formulation termed "strong")? Who coined these terms, and in what sense did they mean that one formulation is stronger than the other? Is it just that the weak formulation has extra solutions which kindof-almost-but-not-strictly satisfy (i.e. weakly satisfy) the original equation?

This concept seems to also be termed the "variational" formulation; does this simply refer to the resemblance of the formulation to the integrals used in variational calculus (introducing an additional arbitrary function, purely as an aid to help solve the original equation)? Cesiumfrog (talk) 08:28, 2 January 2016 (UTC)[reply]