Talk:Korn's inequality

Wrong $$H^1$$ norm?
I think the definition of the $$H^1$$ norm given here is incorrect. The square root on the right-hand side should be over both terms, not over each one individually. I think it should be


 * $$\| v \|_{H^{1} (\Omega)} := \left( \int_{\Omega} \sum_{i = 1}^{n} | v^{i} (x) |^{2} \, \mathrm{d} x + \int_{\Omega} \sum_{i, j = 1}^{n} | \partial_{j} v^{i} (x) |^{2} \, \mathrm{d} x \right)^{1/2}.$$

Am I right? Eriatarka (talk) 17:36, 9 September 2008 (UTC)

You are correct. It has also been changed on the main page as of December 2009. Thanks for pointing it out. 75.177.100.188 (talk) 17:27, 18 August 2012 (UTC)

Sum correct?
Should the sum of the v_i terms in (1) really go over i,j? That means the |v_i|^2 terms will all be counted multiple times (once per j, i.e., n times).

Eponym
The article needs to mention the full name of the person after whom the inequality is named. Solomon7968 16:53, 1 September 2015 (UTC)


 * As far as I can tell it is the physicist https://en.wikipedia.org/wiki/Arthur_Korn who studied (among other things) elasticity around 1908. My search was as follows: https://encyclopediaofmath.org/index.php?title=Korn_inequality#K2 lists two references by "A Korn".  Searching for these references on Google scholar gives relevant results, whose pdfs are available, but the articles only specify the author as "A. Korn".  In the citation information Google Scholar includes the full first name "Arthur".  I'm wary of adding that to Wikipedia because I cannot find an actual journal article (or secondary source) on elasticity with Arthur Korn's full name.  Nevertheless I'm pretty convinced that this is the correct scientist. 89.158.32.119 (talk) 00:07, 17 December 2022 (UTC)