Differentiability properties for a class of non-convex functions

Calculus of Variations and Partial Differential Equations

Volumn 25, Issue 1, 2006, Pages 1-31

  Colombo, Giovanni ^a   Marigonda, Antonio ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 30344454419     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-005-0352-7     Document Type: Article

References (29)

1. Alberti, G., Ambrosio, L., Cannarsa, P.: On the singularities of convex functions, Manuscr. Math. 76, 421-435 (1992)
2. Ambrosio, L.: Corso introduttivo alla Teoria Geometrica della Misura ed alle Superfici Minime, Scuola Normale Superiore, Pisa (1997)
3. Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems, Oxford Science Publications, Clarendon Press, Oxford (2000)
4. Aubin, J.P., Frankowska, H.: Set-Valued Analysis, Birkhäuser, Boston (1990)
5. Bardi, M., Capuzzo-Dolcetta, I.: Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Birkhäuser, Boston (1997)
6. Caffarelli, L., Crandall, M.G., Kocan, M., Swiȩch, A.: On viscosity solutions of fully non-linear equations with measurable ingredients, Comm. Pure Appl. Math. 49, 365-397 (1996)
7. Canino, A.: On p-convex sets and geodesics, J. Differential Equations 75, 118-157 (1988)
8. Canino, A.: Local properties of geodesics on p-convex sets, Ann. Mat. Pura Appl. 159(4), 17-44 (1991)
9. Cannarsa, P., Sinestrari, C.: Semiconcave functions, Hamilton-Jacobi Equations, and Optimal Control, Birkhäuser, Boston (2004)
10. Chlebík, M., Cianchi, A., Fusco, N.: The perimeter inequality for Steiner symmetrization: cases of equality, CVGMT Preprint Server (2002)
11. Clarke, F.H.: Optimization and Nonsmooth Analysis, Wiley, New York (1983)
12. Clarke, F.H., Ledyaev, Yu.S., Stern, R.J., Wolenski, P.R.: Nonsmooth Analysis and Control Theory, Springer, New York (1998)
13. 2 property, J. Convex Anal. 2, 117-144 (1995)
14. Colombo, G., Marigonda, A., Wolenski, P.R.: Some new regularity properties for the minimal time function, SIAM J. Control, to appear
15. Colombo, G., Goncharov, V.V.: Variational Inequalities and Regularity Properties of Closed Sets in Hilbert Spaces, J. Convex Anal. 8, 197-221 (2001)
16. Crandall, M.G., Ishii, H., Lions, P.L.: Users' guide to viscosity solutions of second-order partial differential equations, Bull. Amer. Math. Soc. 27, 1-67 (1992)
17. De Giorgi, E.: Nuovi teoremi relativi alle misure (r -1)-dimensionali in uno spazio a r dimensioni, Ric. Mat. 4, 95-113 (1955)
18. Degiovanni, M., Marino, A., Tosques, M.: General properties of (p, q)-convex functions and (p, q)-monotone operators, Ricerche Mat. 32, 285-319 (1983)
19. Degiovanni, M., Marino, A., Tosques, M.: Evolution equations with lack of convexity, Nonlin. Anal., Th. Meth. Appl. 9, 1401-1443 (1985)
20. Evans, L.C., Gariepy, R.F.: Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton (1992)
21. Falconer, K.: Fractal geometry. Mathematical foundations and applications, Wiley, Chichester (1990)
22. Federer, H.: Curvature Measures, Trans. Amer. Math. Soc. 93, 418-491 (1959)
23. Marino, A., Tosques, M.: Some variational problems with lack of convexity, in Methods of Nonconvex Analysis, Proceedings from CIME, Varenna (1989) (A. Cellina, ed.), Springer, Berlin 58-83 (1990)
24. Mantegazza, C., Mennucci, A.C.: Hamilton-Jacobi equations and distance functions on Riemannian manifolds, Appl. Math. Optim. 47, 1-25 (2003)
25. Poliquin, R.A., Rockafellar, R.T.: Prox-regular functions in variational analysis, Trans. Am. Math. Soc. 348, 1805-1838 (1996)
26. Poliquin, R.A., Rockafellar, R.T., Thibault, L.: Local differentiability of distance functions, Trans. Amer. Math. Soc. 352, 5231-5249 (2000)
27. Rockafellar, R.T.: Convex Analysis, Princeton Univesity Press, Princeton (1972)
28. Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis, Springer, Berlin (1998)
29. Tosques, M.: Equivalence between generalized gradients and subdifferentials for a suitable class of lower semicontinuos functions, in Generalized Convexity, Proceedings, Pécs (1992) (Komlósi, S., Rapcsák, T., Schaible, S., eds.), Springer, Berlin 116-133 (1994)