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In Albano-Cannarsa [1] the authors proved that, under some conditions, the singularities of the semiconcave viscosity solutions of the Hamilton-Jacobi equation propagate along generalized characteristics. In this note we will provide a simple proof of this interesting result.
@article{ASNSP_2006_5_5_4_439_0,
author = {Yu, Yifeng},
title = {A simple proof of the propagation of singularities for solutions of {Hamilton-Jacobi} equations},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {439--444},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 5},
number = {4},
year = {2006},
mrnumber = {2297718},
zbl = {1150.35002},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_4_439_0/}
}
TY - JOUR AU - Yu, Yifeng TI - A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2006 SP - 439 EP - 444 VL - 5 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_4_439_0/ LA - en ID - ASNSP_2006_5_5_4_439_0 ER -
%0 Journal Article %A Yu, Yifeng %T A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2006 %P 439-444 %V 5 %N 4 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_4_439_0/ %G en %F ASNSP_2006_5_5_4_439_0
Yu, Yifeng. A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 4, pp. 439-444. http://geodesic.mathdoc.fr/item/ASNSP_2006_5_5_4_439_0/