Regularity of C 1 solutions of the Hamilton-Jacobi equation

Albert Fathi

Annales de la Faculté des sciences de Toulouse : Mathématiques (2003)

  • Volume: 12, Issue: 4, page 479-516
  • ISSN: 0240-2963

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Fathi, Albert. "Regularity of $C^1$ solutions of the Hamilton-Jacobi equation." Annales de la Faculté des sciences de Toulouse : Mathématiques 12.4 (2003): 479-516. <http://eudml.org/doc/73614>.

@article{Fathi2003,
author = {Fathi, Albert},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Hamilton-Jacobi equation; Euler-Lagrange equation; Legendre transformation},
language = {eng},
number = {4},
pages = {479-516},
publisher = {Université Paul Sabatier, Institut de Mathématiques},
title = {Regularity of $C^1$ solutions of the Hamilton-Jacobi equation},
url = {http://eudml.org/doc/73614},
volume = {12},
year = {2003},
}

TY - JOUR
AU - Fathi, Albert
TI - Regularity of $C^1$ solutions of the Hamilton-Jacobi equation
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2003
PB - Université Paul Sabatier, Institut de Mathématiques
VL - 12
IS - 4
SP - 479
EP - 516
LA - eng
KW - Hamilton-Jacobi equation; Euler-Lagrange equation; Legendre transformation
UR - http://eudml.org/doc/73614
ER -

References

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  6. [Fa] Fathi ( A. ), Théorème KAM faible et Théorie de Mather sur les systèmes lagrangiens, C. R. Acad. Sci. Paris, Série I324, p. 1043-1046 (1997 ). Zbl0885.58022MR1451248
  7. [FI] Fleming ( W.H.), The Cauchy Problem for a nonlinear First Order Partial Diferrential Equation, J. Diff. Equ.5, p. 515-530 (1969). Zbl0172.13901MR235269
  8. [He] Herman ( M.R. ), Inégalités à priori pour des tores lagrangiens invariants par des difféomorphismes symplectiques, Publ. Math. IHES70, p. 47-101 (1989). Zbl0717.58020MR1067380
  9. [Ki] Kiselman ( C.O.), Regularity Classes for Operations in Convexity Theory, Kodai Math. J15, p. 354-374 (1992). Zbl0779.49022MR1189964
  10. [Kn] Knieper ( G.), Mannigfaltigkeiten Ohne Konjugierte Punkte , Bonner Mathematische Shriften168, (1986). Zbl0601.53039MR851010
  11. [La] Lang ( S.) , Differential and Riemannian Manifolds, Third Edition, Graduate Texts in Mathematics160, Springer, New York, Berlin, Heidelberg ( 1995). Zbl0824.58003MR1335233
  12. [Li] Lions ( P.L. ), Generalized Solutions of Hamilton-Jacobi Equations , Research Notes in Mathematics69, Pitman, London ( 1982). Zbl0497.35001MR667669
  13. [Ma] Mather ( J.N. ), Action Minimizing Meausures for Positive Definite Lagrangian Systems, Math. Z.207, p. 169-207 (1991). Zbl0696.58027MR1109661
  14. [PR] Poly( J-B. ) & Raby ( G.), Fonction distance et singularités , Bull. Sci. Math.108, p. 187-195 (1984). Zbl0547.58011
  15. [Ze] Zeghib ( A. ) , Lipschitz Regularity in some Geometric Problems, preprint ENS-Lyon2000 . MR2110754

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