A Sufficient Condition for the C2-Rectifiability of the Set of Regular Values (in the Sense of Clarke) of a Lipschitz Map
Delladio, Silvano
Bollettino dell'Unione Matematica Italiana, Tome 1 (2008), p. 695-707 / Harvested from Biblioteca Digitale Italiana di Matematica

We prove a result about the rectifiability of class C2 of the set of regular values (in the sense of Clarke) of a Lipschitz map φ:nN with n<N

Publié le : 2008-10-01
@article{BUMI_2008_9_1_3_695_0,
     author = {Silvano Delladio},
     title = {A Sufficient Condition for the $C^2$-Rectifiability of the Set of Regular Values (in the Sense of Clarke) of a Lipschitz Map},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {1},
     year = {2008},
     pages = {695-707},
     zbl = {1211.49051},
     mrnumber = {2455340},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2008_9_1_3_695_0}
}
Delladio, Silvano. A Sufficient Condition for the $C^2$-Rectifiability of the Set of Regular Values (in the Sense of Clarke) of a Lipschitz Map. Bollettino dell'Unione Matematica Italiana, Tome 1 (2008) pp. 695-707. http://gdmltest.u-ga.fr/item/BUMI_2008_9_1_3_695_0/

[1] Alberti, G., On the structure of singular sets of convex functions. Calc. Var., 2 (1994), 17-27. | MR 1384392 | Zbl 0790.26010

[2] Anzellotti, G. - Ossanna, E., Singular sets of surfaces with generalized curvatures. Manuscripta Math., 86 (1995), 417-433. | MR 1324680 | Zbl 0837.49020

[3] Anzellotti, G. - Serapioni, R., Ck-rectifiable sets. J. reine angew. Math., 453 (1994), 1-20. | MR 1285779

[4] Bojarski, B. - Hajlasz, P. - Strzelecki, P., Sard's theorem for mappings in Holder and Sobolev spaces. Manuscripta Math., 118, n. 3 (2005), 383-397. | MR 2183045 | Zbl 1098.46024

[5] Clarke, F.H. - Ledyaev, Yu.S. - Stern, R.J. - Wolenski, P.R., Nonsmooth analysis and control theory. Graduate Texts in Mathematics, Springer Verlag 1998. | MR 1488695 | Zbl 1047.49500

[6] Delladio, S., Taylor's polynomials and non-homogeneous blow-ups. Manuscripta Math., 113, n. 3 (2004), 383-396. | MR 2129311 | Zbl 1093.53078

[7] Delladio, S., Non-homogeneous dilatations of a functions graph and Taylors formula: some results about convergence. Real Anal. Exchange, 29, n. 2 (2003/2004), 687-712. | MR 2083806 | Zbl 1071.28005

[8] Delladio, S., A result about C2-rectifiability of one-dimensional rectifiable sets. Application to a class of one-dimensional integral currents. Boll. Un. Matem. Italiana, 10-B (2007), 237-252. | MR 2310966 | Zbl 1178.53003

[9] Delladio, S., A sufficient condition for the CH-rectifiability of Lipschitz curves. To appear on J. Geom. Anal. [PDF available at the page http://eprints.biblio.unitn.it/ archive/00000934/]. | MR 2420763 | Zbl 1152.49325

[10] Evans, L.C. - Gariepy, R.F., Lecture Notes on Measure Theory and Fine Properties of Functions. (Studies in Advanced Math.) CRC Press 1992. | MR 1158660

[11] Federer, H., Geometric Measure Theory. Springer-Verlag1969. | MR 257325 | Zbl 0176.00801

[12] Fu, J.H.G., Some Remarks On Legendrian Rectifiable Currents. Manuscripta Math., 97, n. 2 (1998), 175-187. | MR 1651402 | Zbl 0916.53038

[13] Fu, J.H.G. - Erratum to "Some Remarks On Legendrian Rectifiable Currents". Manuscripta Math., 113, n. 3 (2004), 397-401. | MR 2129312 | Zbl 1066.53014

[14] Mattila, P., Geometry of sets and measures in Euclidean spaces. Cambridge University Press, 1995. | MR 1333890 | Zbl 0819.28004

[15] Simon, L., Lectures on Geometric Measure Theory. Proceedings of the Centre for Mathematical Analysis, Canberra, Australia, vol. 3, 1984. | MR 756417

[16] Stein, E.M., Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, 1970. | MR 290095 | Zbl 0207.13501