i'm interested in the history of the 2 Sobolev Inequalities. The Gagliardo-Nirenberg-Sobolev inequality and Morrey inequality as here Sobolev inequality .

How did these two inequalities arise? What is the context of its emergence? In what year were they discovered?


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    $\begingroup$ The following paper begins with a brief section on the history and motivations of Sobolev spaces. The Sobolev inequalities appear to arise as part of our efforts to find necessary and sufficient conditions for an embedding to be continuous (See section 2.8 on embedding results.) However, since I know nothing about physics and only slightly more about maths, I leave it to you to judge the paper's content and relevance. Please see : home.iitk.ac.in/~tmk/courses/mth656/main.pdf $\endgroup$ – Nick Dec 11 '17 at 18:57
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    $\begingroup$ Possible duplicate of About Sobolev inequalities $\endgroup$ – Elements in Space Dec 16 '17 at 5:55
  • $\begingroup$ There are also early contributions by G. Levi (sometimes called "Beppo") and G. Frobenius, in 1906 and 1907, in the context of proving a (true, as opposed to false) version of the Dirichlet principle. $\endgroup$ – paul garrett Mar 27 '18 at 22:42

The Sobolev Inequality was proved up to a change of coordinates and only for radially symmetric functions by GA Bliss in 1930 (I believe). Sobolev actually did not publish his paper proving the so-called Sobolev Inequality (which does not require radial symmetry) until 1938. I don't know the context for why the inequality was proven. If you have more particular question about further developments of the Sobolev Inequality, let me know.

Anyone know about the history of Morrey's Inequality?

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