Geodesic
Nonconstant Continuous Functions whose Tangential Derivative Vanishes along a Smooth Curve
Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 706-715

Voir la notice de l'article provenant de la source Cambridge

DOI

We provide a simple example showing that the tangential derivative of a continuous function $\phi $ can vanish everywhere along a curve while the variation of $\phi $ along this curve is nonzero. We give additional regularity conditions on the curve and/or the function that prevent this from happening.
DOI : 10.4153/CMB-2011-027-1
Mots-clés : 26A24, 28A15 
Moonens, Laurent. Nonconstant Continuous Functions whose Tangential Derivative Vanishes along a Smooth Curve. Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 706-715. doi: 10.4153/CMB-2011-027-1
@article{10_4153_CMB_2011_027_1,
     author = {Moonens, Laurent},
     title = {Nonconstant {Continuous} {Functions} whose {Tangential} {Derivative} {Vanishes} along a {Smooth} {Curve}},
     journal = {Canadian mathematical bulletin},
     pages = {706--715},
     year = {2011},
     volume = {54},
     number = {4},
     doi = {10.4153/CMB-2011-027-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-027-1/}
}
TY  - JOUR
AU  - Moonens, Laurent
TI  - Nonconstant Continuous Functions whose Tangential Derivative Vanishes along a Smooth Curve
JO  - Canadian mathematical bulletin
PY  - 2011
SP  - 706
EP  - 715
VL  - 54
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-027-1/
DO  - 10.4153/CMB-2011-027-1
ID  - 10_4153_CMB_2011_027_1
ER  - 
%0 Journal Article
%A Moonens, Laurent
%T Nonconstant Continuous Functions whose Tangential Derivative Vanishes along a Smooth Curve
%J Canadian mathematical bulletin
%D 2011
%P 706-715
%V 54
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-027-1/
%R 10.4153/CMB-2011-027-1
%F 10_4153_CMB_2011_027_1

Cité par Sources :