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Difference between revisions of "User talk:Nikita2"

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I saw you texxed the page [[Luzin-C-property]]. I was thinking some time ago to start renaming all pages using Lusin and
 
I saw you texxed the page [[Luzin-C-property]]. I was thinking some time ago to start renaming all pages using Lusin and
 
set automatic redirections for the ones with Luzin. What do you think about it? [[User:Camillo.delellis|Camillo]] ([[User talk:Camillo.delellis|talk]]) 12:10, 25 November 2012 (CET)
 
set automatic redirections for the ones with Luzin. What do you think about it? [[User:Camillo.delellis|Camillo]] ([[User talk:Camillo.delellis|talk]]) 12:10, 25 November 2012 (CET)
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Actually I am not (yet) a ''descendant'' of De Giorgi, I am trying to solve pair of these conjectures.
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I think there should be definitions in more general form: ''if a measurable mapping $f:X\to Y$, $|X|<\infty$ then for any $\varepsilon$ there is an open set $B$ such that the function $f$ is continuous on $B$ and $|X \setminus B|<\varepsilon$''
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The same for N-property. I am going to do it soon. --[[User:Nikita2|Nikita2]] ([[User talk:Nikita2|talk]]) 09:56, 26 November 2012 (CET)

Revision as of 08:56, 26 November 2012

Weighted Sobolev Spaces

Let $D\subset \mathbb R^n$ be open and let $w:\mathbb R^n\rightarrow[0,\infty)$ be a locally summable nonnegative function "weight". For $1\leqslant p<\infty$ and $l\in\mathbb N$ we can define weighted Sobolev space $W^l_p(D,w)$ as the set of locally summable functions $f:D\to\mathbb R$ such that for every multi-index $\alpha$ there exists weak derivative $D^{\alpha}f$ and

\begin{equation} \|f\mid W^l_p(D, w)\| = \Biggl(\,\sum\limits_{|\alpha|\leqslant l}\ \int\limits_{D}|D^{\alpha}f|^p(x)w(x)\, dx \,\Biggr)^{\frac{1}{p}} < \infty. \end{equation}

One of conjectures of De Giorgi

If $\exp(tw), \exp(tw^{-1}) \in L^1_{\operatorname{loc}}$ for each $t > 0$ then $w$ is regular weight.

Welcome

Hello Nikita2 and welcome! Are you also a descendant of De Giorgi?

I saw you texxed the page Luzin-C-property. I was thinking some time ago to start renaming all pages using Lusin and set automatic redirections for the ones with Luzin. What do you think about it? Camillo (talk) 12:10, 25 November 2012 (CET)

Actually I am not (yet) a descendant of De Giorgi, I am trying to solve pair of these conjectures.

I think there should be definitions in more general form: if a measurable mapping $f:X\to Y$, $|X|<\infty$ then for any $\varepsilon$ there is an open set $B$ such that the function $f$ is continuous on $B$ and $|X \setminus B|<\varepsilon$ The same for N-property. I am going to do it soon. --Nikita2 (talk) 09:56, 26 November 2012 (CET)

How to Cite This Entry:
Nikita2. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Nikita2&oldid=28897