Reference request: Expository paper on the use of functional analysis in differential and integral equations

Nobody's said a word about this question, but somebody down-voted it. They didn't explain what was objectionable about it. Can someone?

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    $\begingroup$ I guess this question is way too broad, since "functional analysis", "differential equations" and "integral equations" are enormous subjects, and the literature is huge. For instance, are you interested in elliptic, hyperbolic or parabolic PDE? The methods and the results are very different in the three cases, how can an expository paper cover all of them? The best thing to do is to look at one of the standard textbooks, like Courant-Hilbert, Brezis or Evans, and maybe ask another, more focused question. $\endgroup$ Apr 25 at 7:32
  • $\begingroup$ @FrancescoPolizzi : I had not suspected that anyone would misunderstand the question in the way you do, but now I have edited it further in a way that I hope will make it clearer to anyone who might do that. $\endgroup$ Apr 25 at 18:33
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    $\begingroup$ FWIW I thought the question was also extremely broad, and the people it talked about a very diffuse group. I understood what you meant, but as a non-expert I could still tell it was open to all kinds of different answers based on specific facets of the subjects involved. $\endgroup$
    – David Roberts Mod
    Apr 26 at 6:26
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    $\begingroup$ I agree that there are some deficiencies with the original question, but I'm surprised that this meta question is getting so many downvotes. $\endgroup$ Apr 27 at 16:33
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    $\begingroup$ @TimothyChow The ‘downvote crew’ on MO doesn’t like being asked to justify their downvotes; this question effectively does so. As the kids say, “haters gonna hate”. $\endgroup$
    – Alec Rhea
    Apr 28 at 0:28
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    $\begingroup$ @AlecRhea: the community already discussed a lot about commenting downvotes, see for instance meta.mathoverflow.net/questions/3512/…. The consensus, as far as I know, is that downvotes need not be explained, for a series of reason explained in the post above and in those linked in it. So, what "downvote crew" are you talking about? $\endgroup$ Apr 29 at 5:27
  • $\begingroup$ @FrancescoPolizzi : If downvotes need not ALWAYS be explained, there are still SOME situations where it is inappropriate to omit an explanation. $\endgroup$ Apr 29 at 17:40
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    $\begingroup$ @FrancescoPolizzi Mostly just joking around to show solidarity with Michael, alluding to exactly the precedent you mention that people who downvote routinely around here have decided pretty unanimously that they don’t want to have to explain themselves, which is ultimately fine imo. Best to just keep on keeping on and focus on the mathematics. $\endgroup$
    – Alec Rhea
    Apr 29 at 22:38
  • $\begingroup$ Meta is very often vulgar. $\endgroup$ May 1 at 2:47
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    $\begingroup$ FWIW, I don't see anything objectionable about the question in the post. In response to @FrancescoPolizzi, I don't think something expository needs to be comprehensive; just some examples of samplers of ways that functional analysis can be useful in this way is all I took you to be looking for. But I see that an answer has been given and you have accepted it. If this isn't enough, perhaps the question should include a big-list tag. $\endgroup$
    – Todd Trimble Mod
    May 8 at 2:34
  • $\begingroup$ @ToddTrimble : You are right about the intent of the question. $\endgroup$ May 8 at 17:06


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