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LIST OF PUBLICATIONS

of the professor Mikhail Korobkov
[1] Jean Bourgain, Mikhail V. Korobkov, Jan Kristensen: On the Morse­ Sard property and level sets of W n,1 Sobolev functions on Rn , Journal fur die reine und angewandte Mathematik (Crel les Journal) (Online first), DOI: http://dx.doi.org/10.1515/crelle-2013-0002, March 2013. [2] J. Bourgain, M.V. Korobkov and J. Kristensen: On the Morse­ Sard property and level sets of Sobolev and BV functions, Rev. Mat. Iberoam. 29, no. 1 (2013), 1­23. [3] M.V. Korobkov, J. Kristensen: On the Morse-Sard theorem for the sharp case of Sobolev mappings, to appear in Indiana Univ. Math. J., http://www.iumj.indiana.edu/IUMJ/Preprints/5431.pdf. [4] M.V. Korobkov, K. Pileckas and R. Russo: Solution of Leray's problem for stationary Navier-Stokes equations in plane and axially symmetric spatial domains, to appear in Annals of Math., http://annals.math.princeton.edu/articles/8861 [5] M.V. Korobkov, K. Pileckas and R. Russo, On the flux problem in the theory of steady Navier­Stokes equations with nonhomogeneous boundary conditions, Arch. Rational Mech. Anal. 207 (2013), 185­213. [6] M.V. Korobkov, K. Pileckas and R. Russo: Steady Navier-Stokes system with nonhomogeneous boundary conditions in the axially symmetric case, arXiv:1110.6301, to appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2015), DOI Number: 10.2422/2036-2145.201204 003 [7] M.V. Korobkov, K. Pileckas and R. Russo: The existence of a solution with finite Dirichlet integral for the steady Navier-Stokes equations in a plane exterior symmetric domain, J. Math. Pures. Appl. 101 (2014), 257­274. DOI: http://dx.doi.org/10.1016/j.matpur.2013.06.002 [8] M.V. Korobkov, K. Pileckas and R. Russo, Steady Navier-Stokes system with nonhomogeneous boundary conditions in the axially symmetric case, Comptes rendus ­ Mecanique 340 (2012), 115­119. [9] Korobkov, M. V. Bernoulli law under minimal smoothness assumptions. Dokl. Math. 83 (2011), no.1, 107-110 [10] Korobkov, M. V. Properties of C 1 -smooth functions whose gradient range has topological dimension 1. Dokl. Math. 81 (2010), no.1, 11-13. 1


[11] Korobkov, M. V. Properties of C 1 -smooth mappings with a one-dimensional gradient range. Sib. Math. J. 50 (2009), no. 5, 874-886. [12] Korobkov, M. V. A criterion for the unique determination of domains in Euclidean spaces by the metric of the boundary induced by the intrinsic metric of the domain. Siberian Advances in Math. 20 (2010), no. 4, 256-284. [13] Korobkov, M. V. Necessary and sufficient conditions for the unique determination of plane domains. Sib. Math. J. 49 (2008), no. 3, 436-451. [14] Korobkov, M. V. An example of a C 1 -smooth function whose gradient range is an arc with no tangent at any point. Sib. Math. J. 49 (2008), no. 1, 109-116. [15] Korobkov, M. V. Necessary and sufficient conditions for the unique determination of plane domains. Dokl. Math. 76 (2007), no. 2, 722-723. [16] Korobkov, M. V. Properties of C 1 -smooth functions with a nowhere dense gradient range. Siberian Math. J. 48 (2007), no. 6, 1019-1028. [17] Korobkov, M. V.; Panov, E. Yu. Necessary and sufficient conditions for a curve to be the gradient range of a C 1 -smooth function. Siberian Math. J. 48 (2007), no. 4, 629-647. [18] Korobkov, M. V. Properties of C 1 -smooth functions whose range of the gradient is a nowhere dense set. Dokl. Akad. Nauk 410 (2006), no. 5, 596-598. [19] Korobkov, M. V.; Panov, E. Yu. On necessary and sufficient conditions for a curve to be the range of the gradient of a C 1 -smooth function. Dokl. Akad. Nauk 410 (2006), no. 4, 449-452. [20] Korobkov, M. V. On an analogue of Sard's theorem for C 1 C1-smooth functions of two variables. Siberian Math. J. 47 (2006), no. 5, 889-895. [21] Korobkov, M. V.; Panov, E. Yu. On isentropic solutions of first-order quasilinear equations. Sb. Math. 197 (2006), no. 5-6, 727-752. [22] Korobkov, M. V.; Panov, E. Yu. On the theory of isentropic solutions of quasilinear conservation laws. J. Math. Sci. (N. Y.) 144 (2007), no. 1, 3815-3824. [23] Korobkov, M. On stability of a class of convex functions. Progress in analysis, Vol. I, II (Berlin, 2001), 207-213, World Sci. Publ., River Edge, NJ, 2003. 2


[24] Kopylov, A. P.; Korobkov, M. V.; Ponomarev, S. P. Stability in the Cauchy and Morera theorems for holomorphic functions and their threedimensional analogues. Siberian Math. J. 44 (2003), no. 1, 99-108.
1 [25] Korobkov, M. V. Stability in the C -norm and in the W -norm of classes of Lipschitz functions of one variable. Siberian Math. J. 43 (2002), no. 5, 827-842.

[26] Egorov, A. A.; Korobkov, M. V. On the stability of classes of affine mappings. Siberian Math. J. 42 (2001), no. 6, 1047-1061. [27] Korobkov, M. V. On a generalization of the Lagrange and Darboux theorems to vector-valued functions. Dokl. Akad. Nauk 377 (2001), no. 5, 591-593. [28] Korobkov, M. V. A generalization of Lagrange's mean value theorem to the case of vector-valued mappings. Siberian Math. J. 42 (2001), no. 2, 297-300. [29] Egorov, A. A.; Korobkov, M. V. Stability of classes of Lipschitz mappings, the Darboux theorem, and quasiconvex sets. Siberian Math. J. 41 (2000), no. 5, 855-865. [30] Korobkov, M. V.; Egorov, A. A. Stability of classes of Lipschitz mappings, the Darboux theorem, and quasiconvex sets. Dokl. Akad. Nauk 373 (2000), no. 5, 583-587. [31] Korobkov, M. V. On the stability of classes of Lipschitz mappings generated by compact sets of the space of linear mappings. Siberian Math. J. 41 (2000), no. 4, 656-670. [32] Korobkov, M. V. On a generalization of Darboux's theorem to the multidimensional case. Siberian Math. J. 41 (2000), no. 1, 100-112. [33] Korobkov, M. V. On a generalization of the connectedness concept and its application to differential calculus and to the theory of stability of classes of mappings. Dokl. Akad. Nauk 363 (1998), no. 5, 590-593. [34] M.V. Korobkov, K. Pileckas and R. Russo: The existence theorem for the steady Navier­Stokes problem in exterior axially symmetric 3D domains, arXiv:1403.6921, submitted to Acta Math.

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