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S May 24, 2019 at 8:43 history bounty ended John
S May 24, 2019 at 8:43 history notice removed John
May 21, 2019 at 17:32 vote accept John
May 19, 2019 at 18:21 answer added user128470 timeline score: 3
May 19, 2019 at 14:32 comment added John @user128470 Could you please elaborate more on the role of the condition $\mu>\nu$? And do you want to expand the comment into an answer, so that I can accept it?
May 19, 2019 at 13:16 comment added user128470 I believe that you can just take a compact exhaustion $\Omega_i$ of $\mathbb{R}^n$. On every $\Omega_i$, the weighted norm is equivalent to the usual Soboelv norm. Using Rellich-Kochandrov and a diagonal sequence gives you a converging subsequence, the condition $\mu>\nu$ ensures that the $W_\nu^{1,p}$ norm of the sequence converges to zero outside of the exhaustion.
May 19, 2019 at 12:37 history edited John CC BY-SA 4.0
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S May 19, 2019 at 12:32 history bounty started John
S May 19, 2019 at 12:32 history notice added John Authoritative reference needed
May 19, 2019 at 12:31 history edited John CC BY-SA 4.0
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May 19, 2019 at 11:20 history edited John CC BY-SA 4.0
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May 19, 2019 at 11:07 history edited John CC BY-SA 4.0
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May 15, 2019 at 18:18 history edited John CC BY-SA 4.0
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May 15, 2019 at 7:55 history asked John CC BY-SA 4.0