On the propagation of singularities of semi-convex functions

 Access to full text

 Full (PDF)

1. [1] G. Alberti - L. Ambrosio - P. Cannarsa, On the singularities of convex functions. Manuscripta Math.76 (1992), 421-435. Zbl0784.49011MR1185029
2. [2] L. Ambrosio, Su alcune proprietà delle funzioni convesse. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. (1992) (to appear). 
3. [3] J.P. Aubin - H. Frankowska, Set-Valued Analysis. Birkhäuser, Boston, 1990. Zbl0713.49021MR1048347
4. [4] P. Cannarsa - H.M. Soner, On the singularities of the viscosity solutions to Hamilton - Jacobi Bellman equations. Indiana Univ. Math. J.36 (1987), 501-524. Zbl0612.70016MR905608
5. [5] P. Cannarsa - H.M. Soner, Generalized one-sided estimates for solutions of Hamilton-Jacobi equations and applications. Nonlinear Anal.13 (1989), 305-323. Zbl0681.49030MR986450
6. [6] F.H. Clarke, Optimization and Nonsmooth Analysis. Wiley & Sons, New York, 1983. Zbl0582.49001MR709590
7. [7] M.G. Crandall - L.C. Evans - P.L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Mat. Soc.282 (1984), 487-502. Zbl0543.35011MR732102
8. [8] M.G. Crandall - P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Mat. Soc.277 (1983), 1-42. Zbl0599.35024MR690039
9. [9] I. Ekeland - R. Temam, Convex Analysis and Variational Problems. North-Holland, Amsterdam, 1976. Zbl0322.90046MR463994
10. [10] H. Federer, Geometric Measure Theory. Springer Verlag, Berlin, 1969. Zbl0176.00801MR257325
11. [11] W.H. Fleming, The Cauchy problem for a nonlinear first order partial differential equation. J. Differential Equations5 (1969), 515-530. Zbl0172.13901MR235269
12. [12] H. Ishii, Uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations. Indiana Univ. Math. J.33 (1984), 721-748. Zbl0551.49016MR756156
13. [13] H. Ishii - P.L. Lions, Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. J. Differential Equations83 (1990), 26-78. Zbl0708.35031MR1031377
14. [14] R. Jensen - P.E. Souganidis, A regularity result for viscosity solutions of Hamilton-Jacobi equations in one space dimension. Trans. Amer. Math. Soc.301 (1987), 137-147. Zbl0657.35083MR879566
15. [15] S.N. Kruzkov, Generalized solutions of Hamilton-Jacobi equations of eikonal type I. Math. USSR-Sb.27 (1975), 406-446. Zbl0369.35012
16. [16] P.L. Lions, Generalized solutions of Hamilton-Jacobi equations. Pitman, Boston, 1982. Zbl0497.35001MR667669
17. [17] F. Morgan, Geometric Measure Theory - A beginner's guide. Academic Press, Boston, 1988. Zbl0671.49043MR933756
18. [18] R.T. Rockafellar, Convex Analysis. Princeton University Press, Princeton, 1970. Zbl0193.18401MR274683
19. [19] L. Simon, Lectures on Geometric Measure Theory. Proceedings of the Centre for Mathematical Analysis. Australian National University, Camberra, 1983. Zbl0546.49019MR756417
20. [20] L. Tonelli, Lezioni di Analisi Matematica, vol. I. Tacchi Editrice, Pisa, 1940. JFM67.0151.07
21. [21] M. Tsuji, Formation of singularities for Hamilton-Jacobi equations II. J. Math. Kyoto Univ.26 (1986), 299-308. Zbl0655.35009MR849221

1. Andrea C. G. Mennucci, Regularity and variationality of solutions to Hamilton-Jacobi equations. Part I : regularity
2. Yifeng Yu, A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations
3. Andrea C.G. Mennucci, Regularity and variationality of solutions to Hamilton-Jacobi equations. Part I: Regularity
4. Emmanuel Trélat, Global subanalytic solutions of Hamilton–Jacobi type equations
5. Paolo Albano, Piermarco Cannarsa, Structural properties of singularities of semiconcave functions