Talk:Obstacle problem/GA1

GA Review

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Starting GA review. Jezhotwells (talk) 09:09, 12 July 2009 (UTC)

Quick fail criteria assessment

1. The article completely lacks reliable sources – see Wikipedia:Verifiability.

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2. The topic is treated in an obviously non-neutral way – see Wikipedia:Neutral point of view.

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3. There are cleanup banners that are obviously still valid, including cleanup, wikify, NPOV, unreferenced or large numbers of fact, clarifyme, or similar tags.

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4. The article is or has been the subject of ongoing or recent, unresolved edit wars.

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5. The article specifically concerns a rapidly unfolding current event with a definite endpoint.

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No problems found checking against quick fail criteria. Jezhotwells (talk) 09:12, 12 July 2009 (UTC)

Checking against GA criteria

1. It is reasonably well written.

   a (prose):

   • Not being a mathematician, I find the prose somewhat impenetrable. I am concerned about the large amount of jargon words used here. I will seek help at the Maths project. Jezhotwells (talk) 09:31, 12 July 2009 (UTC)

   b (MoS):

   • Seems OK

2. It is factually accurate and verifiable.

   a (references):

   • I have to assume good faith on the sources. There are a lot of unreferenced statements. Jezhotwells (talk) 09:17, 12 July 2009 (UTC)

   b (citations to reliable sources):

   • I have to assume these are RS Jezhotwells (talk) 09:17, 12 July 2009 (UTC)

   c (OR):

   • I have no opinion on this, hope someone from the maths project can help. Jezhotwells (talk) 09:33, 12 July 2009 (UTC)

3. It is broad in its scope.

   a (major aspects):

   • I don't have any comment on this, will seek advice at Maths project. Jezhotwells (talk) 09:17, 12 July 2009 (UTC)

   b (focused):

   • As per above. Jezhotwells (talk) 09:17, 12 July 2009 (UTC)

4. It follows the neutral point of view policy.

   Fair representation without bias:

   • Apparently

5. It is stable.

   No edit wars etc.:

6. It is illustrated by images, where possible and appropriate.

   a (images are tagged and non-free images have fair use rationales):

   b (appropriate use with suitable captions):

7. Overall:

   Pass/Fail:

   • On hold for second opinion. Jezhotwells (talk) 09:17, 12 July 2009 (UTC)

   (copied from nominator talk page) Um. I just read it, and Geometry Guy is right on every point. It's going to take too long to fix (at least a month, I should think -- I'm going to have to do a good bit of literature survey), and I can't in good conscience ask you to wait. Go ahead and fail it, and I'll work on trying to improve. Getting suggestions for improvement was the purpose of bringing the article to GAR, anyhow. Thanks very much for your efforts. Cheers, RayTalk 23:43, 20 July 2009 (UTC)

   • OK, not listed. Please remember to respond at the review page in future. Perhaps try a peer review before bringing back to GAN. Jezhotwells (talk) 23:57, 20 July 2009 (UTC)

I did some math as an undergrad, but it wasn't the same as this math. I probably understand about half of the wikilinked terms, and less about the obstacle problem. I imagine the math is correct, so we need to think about how to make it a little easier to understand. I guess the first thing I would say, is that some or most wikilinked terms should have a short explanation to go with them. Now, anyone reading this had better have some math in their background, so it doesn't have to make sense to the average adult. It probably won't even make sense to people who have taken calculus. It should make as much sense as possible to people who have gone beyond calc, but don't know about this specific problem. What does that mean? Well, an example is probably the best way to show what I mean. Starting at the top.

The obstacle problem is a classic motivating example in the mathematical study of variational inequalities and free boundary problems. Variational inequalities are all possible solutions to a function that is an inequality that takes in a vector and returns a scalar.

Hopefully that statement is true. ;-) Anyways, short explanations that will orient and remind the reader what each thing is. The article is short, so adding explanations won't make it too long. The explanations may be better in the body than in the lead. Not sure about that. I'll wait for questions/comments before going to far out on a limb here. - Peregrine Fisher (talk) (contribs) 23:52, 19 July 2009 (UTC) One other comment. I was hoping I could just go and grab the first sentence from Variational inequality, and plunk it down, but it didn't really have a GA quality single sentence explanation, without a bit of tweaking. Some of the linked articles may have ready made explanations, or at least close, so doing this hopefully won't be like rewriting the whole article. - Peregrine Fisher (talk) (contribs) 23:55, 19 July 2009 (UTC)

2nd second opinion

It would be remiss of me not to respond to this request, as a mathematician familiar with GA. In my view this article falls significantly short of meeting the GA criteria at the moment and I give my reasons below, along with suggestions for improvements.

• The article relies heavily on a single source, the paper of Caffarelli. This is a fairly recent paper in which (according to Zentralblatt) the author reviews his own work: this is a borderline primary source. I wonder why one of the textbooks is uncited, while the other is cited somewhat sparingly.
• The article is not broad. For instance there is no history of the problem and the applications mentioned in the lead are mostly not covered.
• The lead does not summarize the article. The first two sentences do not define the problem and appear to be unsourced ("classic motivating example" and "deeply related" according to whom?) The article is confused as to whether the obstacle problem is finding solutions or describing their properties (cf. the "Variational inequality" section). Where the lead has "singular points which reside on a smooth manifold", the body has "singular points, which are themselves either isolated or locally contained on a C^1 manifold". Neither of these statements make a great deal of sense, especially not without specifying a dimension: the domain D is a smooth manifold, after all.
• Much of this article should be accessible to a determined reader who knows some multivariate calculus, and most of it should be within reach of an advanced math major. I appreciate that Sobolev spaces are graduate level math, so the article may not be fully accessible to such an audience, but more could be done to circumvent this. There's a good chance that a math major would have met the best approximation theorem for convex sets in Hilbert spaces, so this could be spelled out.
• The article is undercited. For instance in the generalizations section, the last three paragraphs all require citations. In the "Optimal control" section, the source appears not to make the connection with the obstacle problem: such a connection exists, plainly, but Wikipedia readers need a source which makes the connection, not the analysis of Wikipedia's editors.
• The prose is weak. There are many stubby paragraphs. The same notation is used for different functionals. The generalization to coercive bounded bilinear forms is not well explained. Some language is sloppy (e.g. C^{1,1} means bounded second weak derivatives). The caption for the diagram does not explain very well what is going on.
• The image authorship is unclear (hence so is its copyright status). More diagrams and images would be helpful.

So there are issues with pretty much every GA criterion except stability, I'm afraid. Good luck improving the article. Geometry guy 19:21, 20 July 2009 (UTC)

Thanks, Geometry guy. I apprecaite your critique. I will place the article on hold for seven days to allow your points, and those of Peregrine Fisher to be addressed. Jezhotwells (talk) 20:11, 20 July 2009 (UTC)