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A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.

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History of Sobolev space notations

I found this question as I am reading a --mildly old-- paper by Grüter and Widman, "the Green function for uniformly elliptic equations". In the paper, they use the notation $H^1_2$ and $\overset{{\La …
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