Can $u\in W^{1,\infty}\cap H^1(\mathbb R^n)$ be approximated by a sequence $u_k\in C_0^{\infty}(\mathbb R^n)$ with $\|u_k\|_{1,\infty}$ bounded?

Asked Feb 24 '15 at 12:03

Active Feb 24 '15 at 12:03

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This problem is relevant to this but I am not really able to prove it or find a counterexample. Could anyone give a hint?

edited Apr 13 '17 at 12:20

Community

asked Feb 24 '15 at 12:03

tks

1

Find evans book where he proves the approximation theorem. Then look at the construction of approximation functions, you will find how to prove your problem. If you can not do it, let me know and I will write you a answer. – spatially Feb 24 '15 at 17:18
@wisher Thanks for the tip, I think I have it now. I will write a full answer when I find some time. – tks Feb 25 '15 at 17:55

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