# Tagged Questions

For questions about or related to Sobolev spaces, which are function spaces equipped with a norm combining norms of a function and its derivatives.

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### Cauchy sequence in $W^{1,2}$ is Cauchy in $L^2$?

I'm trying to show that the space $W^{1,2}$ is an Hilbert space, i found this answered question: Showing Sobolev space $W^{1,2}$ is a Hilbert space which offer a proof, but I'm having trouble with ...
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### Show that this function is weakly differentiable

I need to show that the function $$u(x_1,x_2) = 1-x_1^2 \quad x_1>0 \\ u(x_1,x_2)=1+x_1^2 \quad x_1 \leq 0$$ is weakly differentiable on the unit ball. It is clear ...
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### Using scaling arguments to determine relationships between Sobolev spaces?

I was looking up how to find relationships between Sobolev spaces and I came across this post on MO in which the first comment talks about a scaling procedure for understanding the relationships: ...
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