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姓名   米哈伊尔

英文名:Mikhail Korobkov

职称:教授

办公室:2117

办公电话:021-55665561

E-mailkorob@math.nsc.ru

研究方向:偏微分方程(partial differential equation), Mathematical analysis, Morse--Sard theorem, Navier--Stokes equations

主讲课程:Sobolev spaces.

代表论著:

List of papers for the last five years:

[1] M.V. Korobkov, K. Pileckas and R. Russo (2015): Solution of Leray’s problem for stationary Navier-Stokes equations in plane and axially symmetric spatial domains, Annals of Math., 181, no. 2, 769-807.
http://dx.doi.org/10.4007/annals.2015.181.2.7

[2] Korobkov M.V., Pileckas K. and Russo R. (2017): The existence theorem for the steady Navier–Stokes problem in exterior axially symmetric 3D domains // Math. Ann. (Online first 2017), http://dx.doi.org/10.1007/s00208-017-1555-x

[3] J. Bourgain, M.V. Korobkov and J. Kristensen (2013): On the Morse– Sard property and level sets of Sobolev and BV functions, Rev. Mat. Iberoam.
29, no. 1, 1–23. http://dx.doi.org/10.4171/rmi/710

[4] Bourgain J., Korobkov M. V., Kristensen J. (2015): On the Morse– Sard property and level sets of Wn,1 Sobolev functions on Rn, Journal fur die reine und angewandte Mathematik (Crelles Journal), 2015, No. 700, 93–112.
http://dx.doi.org/10.1515/crelle-2013-0002

[5] M.V. Korobkov, K. Pileckas and R. Russo (2013): On the flux problem in the theory of steady Navier–Stokes equations with nonhomogeneous boundary conditions, Arch. Rational Mech. Anal. 207, no. 1, 185–213.
http://dx.doi.org/10.1007/s00205-012-0563-y

[6] Korobkov M.V. and Kristensen J. (2017): The Trace Theorem, the Luzin N- and Morse–Sard properties for the sharp case of Sobolev–Lorentz mappings // Journal of Geometric Analysis, (Online first 2017),
http://dx.doi.org/10.1007/s12220-017-9936-7

[7] M.V. Korobkov, K. Pileckas and R. Russo (2012): Steady Navier- Stokes system with nonhomogeneous boundary conditions in the axially symmetric case, Comptes rendus – Mecanique 340, 115–119.

[8] M.V. Korobkov and J.Kristensen (2014): On the Morse-Sard Theorem for the sharp case of Sobolev mappings, Indiana Univ. Math. J., 63, No. 6, 1703–1724. http://dx.doi.org/10.1512/iumj.2014.63.5431

[9] M.V. Korobkov, K. Pileckas and R. Russo (2014): 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, no. 3, 257–274. DOI: http://dx.doi.org/10.1016/j.matpur.2013.06.002

[10] M.V. Korobkov, K. Pileckas, V. V. Pukhnachev, and R. Russo (2014): The flux problem for the Navier-Stokes equations, Russian Math. Surveys, 69, No. 6, 1065–1122.
http://dx.doi.org/10.1070/RM2014v069n06ABEH004928

[11] M.V. Korobkov, K. Pileckas and R. Russo (2015): An existence theorem for steady Navier–Stokes equations in the axially symmetric case, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 14, No. 1 (2015), 233–262.
http://dx.doi.org/10.2422/2036-2145.201204_003

[12] Kopylov A.P., Korobkov M.V. (2015): On properties of the intrinsic geometry of submanifolds in a Riemannian manifold, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, Vol. 31, No. 1, pp. 71–80. http://www.emis.de/journals/AMAPN/vol31_1/31_08.pdf

[13] Korobkov M.V., Tsai T.-P. (2016): Forward Self-Similar Solutions of the Navier-Stokes Equations in the Half Space // Analysis and PDE, V.9, No.8. P.1811–1827. http://dx.doi.org/10.2140/apde.2016.9.1811

[14] Korobkov M.V., Pileckas K., Russo R. (2016): Leray’s Problem on Existence of Steady State Solutions for the Navier-Stokes Flow // in Handbook of Mathematical Analysis in Mechanics, Springer International Publishing AG, Y. Giga, A. Novotny (eds.), P.1-50,  http://dx.doi.org/10.1007/978-3-319-10151-4_5-1

[15] Kopylov, A.P., Korobkov M.V. (2016): Rigidity Conditions for the Boundaries of Submanifolds in a Riemannian Manifold // 
http://dx.doi.org/10.17516/1997-1397-2016-9-3-320-331

[16] Korobkov, M. V. (2011): Bernoulli law under minimal smoothness assumptions. Dokl. Math. 83, no.1, 107-110.
http://dx.doi.org/10.1134/S1064562411010327

[17] Hajlasz P., Korobkov M.V., Kristensen J. (2017): A bridge between Dubovitskii-Federer theorems and the coarea formula // Journal of Functional Analysis, V.272, no. 3, P.1265–1295. http://dx.doi.org/10.1016/j.jfa.2016.10.031

 

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