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.

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.

Classification : 35F20, 35D99 
@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://www.numdam.org/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://www.numdam.org/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://www.numdam.org/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://www.numdam.org/item/ASNSP_2006_5_5_4_439_0/

[1] P. Albano and P. Cannarsa, Propagation of singularities for solutions of nonlinear first order partial differential equations, Arch. Ration. Mech. Anal. 162 (2002), 1-23. | MR | Zbl

[2] P. Albano and P. Cannarsa, Structural properties of singularities of semiconcave functions, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), 719-740. | Numdam | MR | Zbl

[3] L. Ambrosio, P. Cannarsa and H. M. Soner, On the propagation of singularities of semi-convex functions, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 20 (1993), 597-616. | Numdam | MR | Zbl

[4] P. Cannarsa and C. Sinestrari, “Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control”, Progress in Nonlinear Differential Equations and their Applications, Vol. 58, Birkhäuser Boston, Inc., Boston, MA, 2004. | MR | Zbl

[5] L. C. Evans, “Partial Differential Equations”, Graduate Studies in Mathematics, Vol. 19, American Mathematical Society, Providence, RI, 1998. | MR | Zbl