# A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2006)

- Volume: 5, Issue: 4, page 439-444
- ISSN: 0391-173X

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topYu, 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 5.4 (2006): 439-444. <http://eudml.org/doc/241806>.

@article{Yu2006,

abstract = {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.},

author = {Yu, Yifeng},

journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},

language = {eng},

number = {4},

pages = {439-444},

publisher = {Scuola Normale Superiore, Pisa},

title = {A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations},

url = {http://eudml.org/doc/241806},

volume = {5},

year = {2006},

}

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

PB - Scuola Normale Superiore, Pisa

VL - 5

IS - 4

SP - 439

EP - 444

AB - 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.

LA - eng

UR - http://eudml.org/doc/241806

ER -

## References

top- [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. Zbl1043.35052MR1892229
- [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. Zbl0957.26002MR1760538
- [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. Zbl0874.49041MR1267601
- [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. Zbl1095.49003MR2041617
- [5] L. C. Evans, “Partial Differential Equations”, Graduate Studies in Mathematics, Vol. 19, American Mathematical Society, Providence, RI, 1998. Zbl0902.35002MR1625845

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