# A note on propagation of singularities of semiconcave functions of two variables

Commentationes Mathematicae Universitatis Carolinae (2010)

- Volume: 51, Issue: 3, page 453-458
- ISSN: 0010-2628

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topZajíček, Luděk. "A note on propagation of singularities of semiconcave functions of two variables." Commentationes Mathematicae Universitatis Carolinae 51.3 (2010): 453-458. <http://eudml.org/doc/38141>.

@article{Zajíček2010,

abstract = {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.},

author = {Zajíček, Luděk},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {semiconcave functions; singularities; semiconcave function; singularity},

language = {eng},

number = {3},

pages = {453-458},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A note on propagation of singularities of semiconcave functions of two variables},

url = {http://eudml.org/doc/38141},

volume = {51},

year = {2010},

}

TY - JOUR

AU - Zajíček, Luděk

TI - A note on propagation of singularities of semiconcave functions of two variables

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2010

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 51

IS - 3

SP - 453

EP - 458

AB - 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.

LA - eng

KW - semiconcave functions; singularities; semiconcave function; singularity

UR - http://eudml.org/doc/38141

ER -

## References

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