| Title:
|
A note on propagation of singularities of semiconcave functions of two variables (English) |
| Author:
|
Zajíček, Luděk |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
453-458 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
P. Albano and P. Cannarsa proved in 1999 that, under some applicable conditions, singularities of semiconcave functions in $\mathbb R^n$ propagate along Lipschitz arcs. Further regularity properties of these arcs were proved by P. Cannarsa and Y. Yu in 2009. We prove that, for $n=2$, these arcs are very regular: they can be found in the form (in a suitable Cartesian coordinate system) $\psi(x) = (x, y_1(x)-y_2(x))$, $x\in [0,\alpha]$, where $y_1$, $y_2$ are convex and Lipschitz on $[0,\alpha]$. In other words: singularities propagate along arcs with finite turn. (English) |
| Keyword:
|
semiconcave functions |
| Keyword:
|
singularities |
| MSC:
|
26B25 |
| MSC:
|
35A21 |
| idZBL:
|
Zbl 1224.26047 |
| idMR:
|
MR2741878 |
| . |
| Date available:
|
2010-09-02T14:16:24Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140721 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| . |
