# Questions tagged [sobolev-spaces]

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

3,529 questions
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### Technique to prove existence?

I would like to prove the existence of a T-periodic function $v$ in $H^1(R^N)$ s.t. $v=|v|e^{i\theta}$ for some T-periodic $\theta \in H^1(R^N)$ and s.t. one certain functional $I_c$ turns negative at ...
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### If $v\in H^1(]0,1[)$, then $|v(\lambda)| \leq ||v||_{L^1(]0,1[)} + ||v'||_{L^2(]0,1[)}$

Let $v\in H^1(]0,1[)$. I want to prove for all $\lambda \in [0,1]$ that, $$|v(\lambda)| \leq ||v||_{L^1(]0,1[)} + ||v'||_{L^2(]0,1[)}$$ My idea : I defined $u(\lambda)= \int_0^{\lambda}v'(t)dt$ ...
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### Is the projection onto the unit circle Sobolev?

Let $f(x,y)=\frac{x}{\sqrt{x^2+y^2}}$. Does $f \in W^{1,p}(B)$ for some $p \ge 1$, where $B$ is the open unit disk in $\mathbb{R}^2$? (I guess we can replace $B$ with a disk with arbitrarily small ...
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### If $f\in C(U)$, then $f^{\epsilon }\to f$ uniformly on compact subsets of $U$

If $f\in C(U)$, then $f^{\epsilon }\to f$ uniformly on compact subsets of $U$ my Question how he says that $f$ is uniformly on $W$ i am so learner and the only hope i learn sobolev spaces is ...
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### How to study SOBOLEV SPACES in Evans PDE [closed]

Im New here can you some one suggest me how to study sobolev spaces i am almost studied from one month im not getting any thing is any videos are there and is any one teach sobolev space (any tutor ...
here my question is what is mean by $f^{\epsilon}:=\eta_{\epsilon}*f$ in $U_{\epsilon}$ and how can we change form $U$ to $B(0,\epsilon)$ in the molification definition and what is use convolution ...