Structural properties of singularities of semiconcave functions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 28 (1999) no. 4, p. 719-740
@article{ASNSP_1999_4_28_4_719_0,
     author = {Albano, Paolo and Cannarsa, Piermarco},
     title = {Structural properties of singularities of semiconcave functions},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 28},
     number = {4},
     year = {1999},
     pages = {719-740},
     zbl = {0957.26002},
     mrnumber = {1760538},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1999_4_28_4_719_0}
}
Albano, Paolo; Cannarsa, Piermarco. Structural properties of singularities of semiconcave functions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 28 (1999) no. 4, pp. 719-740. http://www.numdam.org/item/ASNSP_1999_4_28_4_719_0/

[1] P. Albano - P. Cannarsa, Singularities of semiconcave functions in Banach spaces, In: " Stochastic Analysis, Control, Optimization and Applications", W. M. McENEANEY - G. G. YIN - Q. ZHANG (eds.), Birkhäuser, Boston, 1999, pp. 171-190. | MR 1702959 | Zbl 0923.49010

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

[3] G. Alberti - L. Ambrosio - P. Cannarsa, On the singularities of convex functions, Manuscripta Math. 76 (1992), 421-435. | MR 1185029 | Zbl 0784.49011

[4] L. Ambrosio - P. Cannarsa - H.M. Soner, On the propagation of singularities of semi-convex functions, Annali Scuola Norm. Sup. Pisa Cl. Sci. (4) 20 (1993), 597-616. | Numdam | MR 1267601 | Zbl 0874.49041

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

[6] M. Bardi - I. Capuzzo Dolcetta, "Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations", Birkhduser, Boston, 1997. | MR 1484411 | Zbl 0890.49011

[7] K. Bartke - H. Berens, Eine beschreibung der nichteindeutigkeitsmenge für die beste approximation in der euklidischen ebene, J. Approx. Theory 47 (1986), 54-74. | MR 843455 | Zbl 0619.41020

[8] P. Cannarsa - H. Frankowska, Some characterizations of optimal trajectories in control theory, SIAM J. Control Optim. 29 (1991), 1322-1347. | MR 1132185 | Zbl 0744.49011

[9] P. Cannarsa - C. Sinestrari, Convexity properties of the minimum time function, Calc. Var. Partial Differential Equations 3 (1995), 273-298. | MR 1385289 | Zbl 0836.49013

[10] 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. | MR 905608 | Zbl 0612.70016

[11] F.H. Clarke - YU. S. LEDYAEV - R.J. Stern - P.R. Wolenski, "Nonsmooth analysis and control theory", Graduate Texts in Mathematics, Springer, New York, 1998. | MR 1488695 | Zbl 1047.49500

[12] M.G. Crandall - L.C. Evans - P.L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 282 (1984), 487-502. | MR 732102 | Zbl 0543.35011

[13] M.G. Crandall - H. Ishii - P.L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1992), 1-67. | MR 1118699 | Zbl 0755.35015

[14] M.G. Crandall - P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), 1-42. | MR 690039 | Zbl 0599.35024

[15] A. Douglis, The continuous dependence of generalized solutions of non-linear partial differential equations upon initial data, Comm. Pure Appl. Math. 14 (1961), 267-284. | MR 139848 | Zbl 0117.31102

[16] P. Erdös, Some remarks on the measurability of certain sets, Bull. Amer. Math. Soc. 51 (1945), 728-731. | MR 13776 | Zbl 0063.01269

[17] W.H. Fleming, "Functions of several variables", Springer, New York, 1977. | MR 422527 | Zbl 0348.26002

[18] W.H. Fleming - H.M. Soner, "Controlled Markov processes and viscosity solutions", Springer, Berlin, 1993. | MR 1199811 | Zbl 0773.60070

[19] L. Hörmander, "Notions of convexity", Birkhäuser, Boston, 1994. | MR 1301332 | Zbl 0835.32001

[20] S.N. Kruzhkov, Generalized solutions of Hamilton-Jacobi equations of the eikonal type I, Math. USSR Sb. 27 (1975), 406-445.

[21] H. Ishii, Uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations, Indiana Univ. Math. J. 33 (1984), 721-748. | MR 756156 | Zbl 0551.49016

[22] P.L. Lions, "Generalized solutions of Hamilton-Jacobi equations", Pitman, Boston, 1982. | MR 667669 | Zbl 0497.35001

[23] Th. Motzkin, Sur quelques propriétés caractéristiques des ensembles convexes, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 21 (1935), 562-567. | Zbl 0011.41105

[24] A.I. Subbotin, "Generalized solutions of first order PDEs: the dynamic optimization perspective", Birkhduser, Boston, 1995. | MR 1320507 | Zbl 0820.35003

[25] L. Veselý, On the multiplicity points of monotone operators on separable Banach spaces, Comment. Math. Univ. Carolin. 27 (1986), 551-570. | MR 873628 | Zbl 0616.47043

[26] L. Veselý, On the multiplicity points of monotone operators on separable Banach spaces II, Comment. Math. Univ. Carolin. 28 (1987), 295-299. | MR 904754 | Zbl 0644.47047

[27] L. Veselý, A connectedness property of maximal monotone operators and its application to approximation theory, Proc. Amer. Math. Soc. 115 (1992), 663-667. | MR 1095227 | Zbl 0762.47024

[28] U. Westphal - J. Frerking, On a property of metric projections onto closed subsets of Hilbert spaces, Proc. Amer. Math. Soc. 105 (1989), 644-651. | MR 946636 | Zbl 0676.41036

[29] L Zajíček, On the points of multiplicity of monotone operators, Comment. Math. Univ. Carolin. 19 (1978), 179-189. | MR 493541 | Zbl 0404.47025

[30] L Zajíček, On the differentiation of convex functions in finite and infinite dimensional spaces, Czechoslovak Math. J. 29 (1979), 340-348. | MR 536060 | Zbl 0429.46007