Regularity of $C^1$ solutions of the Hamilton-Jacobi equation

Albert Fathi

Regularity of

C^{1}

solutions of the Hamilton-Jacobi equation

Albert Fathi

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 12 (2003) no. 4, pp. 479-516.

MR Zbl

@article{AFST_2003_6_12_4_479_0,
     author = {Albert Fathi},
     title = {Regularity of $C^1$ solutions of the {Hamilton-Jacobi} equation},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {479--516},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 12},
     number = {4},
     year = {2003},
     zbl = {1059.37047},
     mrnumber = {2060597},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2003_6_12_4_479_0/}
}

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PB  - Université Paul Sabatier, Institut de Mathématiques
PP  - Toulouse
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%D 2003
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Albert Fathi. Regularity of $C^1$ solutions of the Hamilton-Jacobi equation. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 12 (2003) no. 4, pp. 479-516. https://afst.centre-mersenne.org/item/AFST_2003_6_12_4_479_0/

Bibliographie
Cité par

[Be] Benton Jr.( S.H.), The Hamilton-Jacobi Equation: A Global Approach, Academic Press, New York , San Francisco, and London , Mathematics in Science and Enggineering 131, (1977). | MR | Zbl

[BP] Bialy (M. ) & Polterovitch (L.), Hamiltonian Diffeomorphisms and Lagrangian Distributions, Math. Zeitschrift 2, p. 173-210 (1992). | Zbl

[CC] Caffarelli ( L.A. ) & Cabré (X.), Fully Nonlinear Elliptic Equations , Colloquium Publications43, AMS, Providence (1995 ). | Zbl

[CI] Clarke ( F.H. ) , Methods of Dynamic and Nonsmooth Optimization , CBMS-NSF Regional Conference Series in Applied Mathematics 57 , SIAM, Philadelphia (1989). | MR | Zbl

[Es] Eschenburg ( J.H. ), Horospheres and the Stable Part of the Geodesic Flow, Math. Zeitschrift 153, p. 237-251 (1977). | MR | Zbl

[Fa] Fathi (A. ), Théorème KAM faible et Théorie de Mather sur les systèmes lagrangiens, C. R. Acad. Sci. Paris, Série I 324, p. 1043-1046 (1997 ). | MR | Zbl

[FI] Fleming ( W.H.), The Cauchy Problem for a nonlinear First Order Partial Diferrential Equation, J. Diff. Equ. 5, p. 515-530 (1969). | MR | Zbl

[He] Herman (M.R. ), Inégalités à priori pour des tores lagrangiens invariants par des difféomorphismes symplectiques, Publ. Math. IHES 70, p. 47-101 (1989). | Numdam | MR | Zbl

[Ki] Kiselman ( C.O.), Regularity Classes for Operations in Convexity Theory, Kodai Math. J 15, p. 354-374 (1992). | MR | Zbl

[Kn] Knieper ( G.), Mannigfaltigkeiten Ohne Konjugierte Punkte , Bonner Mathematische Shriften 168, (1986). | MR | Zbl

[La] Lang (S.) , Differential and Riemannian Manifolds, Third Edition, Graduate Texts in Mathematics 160, Springer, New York, Berlin, Heidelberg ( 1995). | MR | Zbl

[Li] Lions (P.L. ), Generalized Solutions of Hamilton-Jacobi Equations , Research Notes in Mathematics 69, Pitman, London ( 1982). | MR | Zbl

[Ma] Mather (J.N. ), Action Minimizing Meausures for Positive Definite Lagrangian Systems, Math. Z. 207, p. 169-207 (1991). | EuDML | MR | Zbl

[PR] Poly( J-B. ) & Raby (G.), Fonction distance et singularités , Bull. Sci. Math. 108, p. 187-195 (1984). | Zbl

[Ze] Zeghib ( A. ) , Lipschitz Regularity in some Geometric Problems, preprint ENS-Lyon 2000 . | MR | Zbl