References

 Kruzhkov S.N. Generalized solutions of the HamiltonJacobi equations of eikonal type. I. Formulation of the problems; existence, uniqueness and stability theorems; some properties of the solutions, Mathematics of the USSRSbornik, 1975, vol. 27, no. 3, pp. 406446. DOI: 10.1070/SM1975v027n03ABEH002522
 Crandall M.G., Lions P.L. Viscosity solutions of HamiltonJacobi equations, Transactions of the American Mathematical Society, 1983, vol. 277, no. 1, pp. 142. DOI: 10.1090/S00029947198306900398
 Subbotin A.I. Generalized solutions of first order PDEs: the dynamical optimization perspective, Boston: Birkhäuser, 1995, XII+314 p. DOI: 10.1007/9781461208471
 Krasovskii N.N., Subbotin A.I. Pozitsionnye differentsial'nye igry (Positional differential games), Moscow: Nauka, 1974, 456 p.
 Grigor’eva S.V., Pakhotinskikh V.Yu., Uspenskii A.A., Ushakov V.N. Construction of solutions in certain differential games with phase constraints, Sbornik: Mathematics, 2005, vol. 196, no. 4, pp. 513539. DOI: 10.1070/SM2005v196n04ABEH000890
 Lebedev P.D., Uspenskii A.A., Ushakov V.N. Construction of a minimax solution for an eikonaltype equation, Proceedings of the Steklov Institute of Mathematics, 2008, vol. 263, suppl. 2, pp. S191S201. DOI: 10.1134/S0081543808060175
 Uspenskii A.A., Lebedev P.D. Construction of the optimal outcome function for a timeoptimal problem on the basis of a symmetry set, Automation and Remote Control, 2009, vol. 70, no. 7, pp. 11321139. DOI: 10.1134/S0005117909070054
 Uspenskii A.A., Lebedev P.D. On the set of limit values of local diffeomorphisms in wavefront evolution, Proceedings of the Steklov Institute of Mathematics, 2011, vol. 272, suppl. 1, pp. S255S270. DOI: 10.1134/S0081543811020180
 Uspenskii A.A. Calculation formulas for nonsmooth singularities of the optimal result function in a timeoptimal problem, Proceedings of the Steklov Institute of Mathematics, 2015, vol. 291, suppl. 1, pp. S239S254. DOI: 10.1134/S0081543815090163
 Uspenskii A.A., Lebedev P.D. The construction of singular curves for generalized solutions of eikonaltype equations with a curvature break in the boundary of the edge set, Proceedings of the Steklov Institute of Mathematics, 2017, vol. 297, suppl. 1, pp. S191S202. DOI: 10.1134/S0081543817050212
 Uspenskii A.A. Necessary conditions for the existence of pseudovertices of the boundary set in the Dirichlet problem for the eikonal equation, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 2015, vol. 21, no. 1, pp. 250263 (in Russian).
 Arnold V.I. Singularities of caustics and wave fronts, Springer Netherlands, 1990, XIII+259 p. DOI: 10.1007/9789401133302
 Zakalyukin V.M., Kurbatskii A.N. Envelope singularities of families of planes in control theory, Proceedings of the Steklov Institute of Mathematics, 2008, vol. 262. issue 1, pp. 6679. DOI: 10.1134/S0081543808030073
 Borovskikh A.V. Equivalence groups of eikonal equation and classes of equivalent equations, Vestnik Novosibirskogo Gosudarstvennogo Universiteta, 2006, no. 4, pp. 342 (in Russian).
 Sethian J.A., Vladimirsky A. Fast methods for the Eikonal and related HamiltonJacobi equations on unstructured meshes, Proc. Natl. Acad. Sci. USA, 2000, vol. 97, no. 11, pp. 56995703. DOI: 10.1073/pnas.090060097
 Uspenskii A.A., Ushakov V.N., Fomin A.N. $\alpha$sets and their properties, Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 2004, 62 p. Deposited in VINITI 02.04.2004, no. 543В2004 (in Russian).
 Ushakov V.N., Uspenskii A.A. $\alpha$sets in finite dimensional Euclidean spaces and their properties, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 1, pp. 95120. DOI: 10.20537/vm160109
 Bruce J.W., Giblin P.J. Curves and singularities, Cambridge: Cambridge University Press, 1984, 222 p. Translated under the title Krivye i osobennosti, Moscow: Mir, 1988, 262 p.
 Uspenskii A.A. Derivatives with respect to diffeomorphisms and their applications in control theory and geometrical optics, Proceedings of the Steklov Institute of Mathematics, 2016, vol. 293, suppl. 1, pp. 238253. DOI: 10.1134/S0081543816050217
 Ohm M. Lehrbuch der gesamten höhern Mathematik. Bd. 2., Leipzig: Verlag Friedrich Volckmar, 1835.
