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

Yifeng Yu

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

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

Abstract

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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.

How to cite

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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 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

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  1. [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. [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. [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. [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. [5] L. C. Evans, “Partial Differential Equations”, Graduate Studies in Mathematics, Vol. 19, American Mathematical Society, Providence, RI, 1998. Zbl0902.35002MR1625845

Citations in EuDML Documents

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  1. Jean-Pierre Serre, Travaux de Baker
  2. Dimitrios Poulakis, Solutions entières de l’équation Y m = f ( X )
  3. N. Saradha, T.N. Shorey, R. Tijdeman, On the equation x(x+1)... (x+k-1) = y(y+d)... (y+(mk-1)d), m=1,2
  4. N. Saradha, On blocks of arithmetic progressions with equal products
  5. Gary Walsh, The Diophantine equation X² - db²Y⁴ = 1
  6. Wolfgang M. Schmidt, Integer points on curves of genus 1
  7. Maohua Le, A note on the integer solutions ofhyperelliptic equations
  8. Piermarco Cannarsa, Generalized gradient flow and singularities of the Riemannian distance function
  9. R. Balasubramanian, T. N. Shorey, Squares in products from a block of consecutive integers
  10. Michel Langevin, Quelques applications de nouveaux résultats de van der Poorten

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