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I cannot find a reference anywhere to a proof of this result. I am interested in a reference to a proof of this result, and I think it will improve the article for future readers who (like me) wonder how this result is proved. [[User:John Smith Anderson|John Smith Anderson]] ([[User talk:John Smith Anderson|talk]]) 11:59, 14 June 2020 (UTC)
:This is essentially Problem 1.1 in "Numerical Solution of Partial Differential Equations by the Finite Element Method" by Claes Johnson. (1) implies that u"-f is orthogonal to any v. Pick any point x inside the interval and restrict v to have support in delta-neighborhood of x. By the mean value theorem for integrals, there is a point c in that delta-neighborhood such that (u"-f)v is zero at c, i.e. such that (u"-f)(c)=0. Now by continuity (u"-f)(x)=0 which implies P1 since x was arbitrary. [[User:Tzanio|Tzanio]] ([[User talk:Tzanio|talk]]) 03:01, 10 July 2020 (UTC)
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