Tuesday, 31 January 2012

fa.functional analysis - A question on weak derivative - Sobolev spaces

Let Omega be an open set in Rn, and finL1loc(Omega), such that foreach multiindex alphainNn, |alpha|=l f has weak derivative Dalphaf in Lp(Omega), with 1leqpleqinfty.



In general it is not true that finLp(Omega), but it have to be true that finLploc(Omega). How can be shown that?

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