A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 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
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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, Serie 5, Volume 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