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| bio | website | |
|---|---|---|
| location | ||
| age | ||
| visits | member for | 8 months |
| seen | 4 hours ago | |
| stats | profile views | 29 |
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1d |
revised |
Extension Thoerem for the Sobolev Space $W^{1, \infty}(U)$ added 146 characters in body |
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1d |
answered | Extension Thoerem for the Sobolev Space $W^{1, \infty}(U)$ |
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May 15 |
awarded | Caucus |
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Apr 30 |
accepted | The definition of $p$ capacity of a set $A\subset\mathbb{R}^n$ |
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Apr 30 |
asked | The definition of $p$ capacity of a set $A\subset\mathbb{R}^n$ |
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Apr 29 |
comment |
Which mathematicians have influenced you the most? ...he used to divide by zero in his Calculus:) |
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Apr 28 |
comment |
Concerning the noncompactness of the map, $I: W^{1, 2}(\mathbb{R}^n)\rightarrow L^{2^{\ast}}(\mathbb{R}^n)$ This is the set\begin{equation} L^{2^{\ast}}(\mathbb{R}^n)=\left\{f: \mathbb{R}^n\rightarrow\mathbb{R}\ \vert\ f\text{ is measurable wrt Lesbegue n-dim. measure and } \left[\int_{\mathbb{R}^n} \vert f(x)\vert^{2^{\ast}}\text{ d}x\right]^{1/2^{\ast}}<\infty \right\}\end{equation} where \begin{equation} 2^{\ast}\equiv\frac{2n}{n-2}.\end{equation} |
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Apr 28 |
accepted | Concerning the noncompactness of the map, $I: W^{1, 2}(\mathbb{R}^n)\rightarrow L^{2^{\ast}}(\mathbb{R}^n)$ |
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Apr 28 |
comment |
Concerning the noncompactness of the map, $I: W^{1, 2}(\mathbb{R}^n)\rightarrow L^{2^{\ast}}(\mathbb{R}^n)$ Thanks, I fixed a couple of the things in my question which you said. It is a fact that $I$ is not compact but I am working on a characterisation of this noncompactness right now and so I've left the word 'suppose' to remind/emphasize the direction of the iff proof I'm trying to prove. My wrong negation of compactness made the actual stuff that I wanted to do with this information harder. But things are more straightforward now and getting the above results for a subsequence is sufficient. Cheers. |
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Apr 28 |
revised |
Concerning the noncompactness of the map, $I: W^{1, 2}(\mathbb{R}^n)\rightarrow L^{2^{\ast}}(\mathbb{R}^n)$ added 1 characters in body |
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Apr 28 |
revised |
Concerning the noncompactness of the map, $I: W^{1, 2}(\mathbb{R}^n)\rightarrow L^{2^{\ast}}(\mathbb{R}^n)$ added 1 characters in body |
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Apr 28 |
revised |
Concerning the noncompactness of the map, $I: W^{1, 2}(\mathbb{R}^n)\rightarrow L^{2^{\ast}}(\mathbb{R}^n)$ added 14 characters in body |
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Apr 27 |
asked | Concerning the noncompactness of the map, $I: W^{1, 2}(\mathbb{R}^n)\rightarrow L^{2^{\ast}}(\mathbb{R}^n)$ |
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Apr 20 |
revised |
Triangle inequality: $\vert\vert a+b\vert^q-\vert a\vert^q\vert\leq \varepsilon\vert a\vert^q+C(\varepsilon)\vert b\vert^q$ added 2 characters in body; edited title |
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Apr 20 |
comment |
Triangle inequality: $\vert\vert a+b\vert^q-\vert a\vert^q\vert\leq \varepsilon\vert a\vert^q+C(\varepsilon)\vert b\vert^q$ Yes, I mean $\vert\vert a+b\vert^q-\vert a\vert^q\vert$, sorry for the typo. It's fixed now. Thanks. |
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Apr 20 |
revised |
Triangle inequality: $\vert\vert a+b\vert^q-\vert a\vert^q\vert\leq \varepsilon\vert a\vert^q+C(\varepsilon)\vert b\vert^q$ edited tags; edited title |
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Apr 20 |
asked | Triangle inequality: $\vert\vert a+b\vert^q-\vert a\vert^q\vert\leq \varepsilon\vert a\vert^q+C(\varepsilon)\vert b\vert^q$ |
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Apr 13 |
accepted | Proof of Lemma 4.2 in [G-T] pg 55 |
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Apr 13 |
comment |
Proof of Lemma 4.2 in [G-T] pg 55 Lets see\begin{equation}\int_{\Omega_0} \frac{\partial\Phi}{\partial y_j\partial y_i}\eta_{\varepsilon}\text{ d}y=-\int_{\Omega_0}\frac{\partial\Phi}{\partial y_i}\frac{\partial\eta_{\varepsilon}}{\partial y_j}\text{ d}y+\int_{\partial\Omega_0}\frac{\partial\Phi}{\partial y_i}\eta_{\varepsilon}\nu^{j}\text{ d}S_y\end{equation}... I can't believe I missed that...thanks James! |
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Apr 13 |
revised |
Proof of Lemma 4.2 in [G-T] pg 55 fixed typo |
