K. Khanin, A. Sobolevski, “On Dynamics of Lagrangian Trajectories for Hamilton–Jacobi Equations”, Archive for Rational Mechanics and Analysis, 2015, 1–25 (to appear) , arXiv: 1211.7084
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Fréchet Barycenters and a Law of Large Numbers for Measures on the Real Line, e-print arXiv:1512.08421 [math.PR], 17 pp.
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Scientific Activity of Alfred Yarbus: The Stages of Research Work, Senior and Younger Colleagues, Conditions of Investigations // Perception, 2015, 44(8-9), P. 837-850.
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G. L. Litvinov, A. Ya. Rodionov, S. N. Sergeev, A. N. Sobolevski, “Universal algorithms for solving the matrix Bellman equations over semirings”, Soft Computing, 17:10 (2013), 1767–1785
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Planar diagrams form optimization. Preprint arXiv:1203.3248 (submitted).
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Droplet condensation and isoperimetric towers, Pacific J. Math., in press (preprint: http://cvgmt.sns.it/paper/1784/).

Universal algorithms for solving the matrix Bellman equations over semirings. Preprint arXiv:1209.5011
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Minimum-weight perfect matching for non-intrinsic distances on the line // Zapiski nauchnyh seminarov POMI, v. 390 (2011) 52-68.
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Universal Algorithms, Mathematics of Semirings and Parallel Computations. In: COPING WITH COMPLEXITY: MODEL REDUCTION AND DATA ANALYSIS Lecture Notes in Computational Science and Engineering, 2011, Volume 75, 63-89, DOI: 10.1007/978-3-642-14941-2_4
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Indicateurs d"appariement locaux pour le transport optimal en coût concave, ROADEF 2010 : 11ème congrès de la Société Française de Recherche Opérationnelle et d"Aide à la Décision, Toulouse, 24–26 février 2010.

Local matching indicators for concave transport costs, C. R. Acad. Sci. Paris, Ser. I 348 (2010) 901–905 (doi:10.1016/j.crma.2010.07.010).
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Ballistic deposition patterns beneath a growing Kardar-Parisi-Zhang interface, Phys. Rev. E 82 (2010) 061107 (preprint arXiv:1006.4576).
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Particle dynamics inside shocks in Hamilton–Jacobi equations, Theme Issue “Turbulent Mixing and Beyond,” Philosophical Transactions of Royal Society London, 368:1916 (2010) 1579-1593 (doi:10.1098/rsta.2009.0283, preprint arXiv:1001.0498).
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Fast transport optimization for Monge costs on the circle SIAM J. Appl. Math. 70:7 (2010) 2239–2258 (doi:10.1137/090772708, preprint hal-00362834).
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Convex analysis, tropical algebra, and processing of astronomical data. In: Mathematical Forum, vol. 2: Studies in Convex Analysis. V. M. Tikhomirov, ed. Vladikavkaz, 2009. Pp. 230-233 (in Russian).

The Monge-Ampère-Kantorovich approach to reconstruction in cosmology. Phys. D. 237:14-17 (2008), 2145-2150. [See also http://arxiv.org/abs/0712.2561]
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Ballistic aggregation in symmetric and nonsymmetric flows. J. Exper. Theor. Phys. 104:6 (2007), 887-896. [Russian original: Андриевский А. А., Гурбатов С. Н., Соболевский А. Н. Баллистическая агрегация в симметричных и несимметричных течениях. ЖЭТФ 131:6 (2007) 1018-; see also http://arxiv.org/abs/nlin.PS/0601006]
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A variational approach to the reconstruction of galactic peculiar velocities. Mosc. U. Phys. Bull. 62:3 (2007), 147-150. [Russian original: Курносов А. А., Соболевский А. Н. Вариационный подход к реконструкции пекулярных скоростей галактик. Вестник Московского университета 62:3 (2007), 18-21.]
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Application of optimal transport theory to reconstruction of the early Universe. J. Math. Sci. 133:4 (2006), 1539-1542.
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A blow-up phenomenon in the Hamilton-Jacobi equation in an unbounded domain. In: Idempotent mathematics and mathematical physics. Vol. 377 of Contemp. Math. Amer. Math. Soc., Providence, RI, 2005, pp. 161-179. [See also: http://arxiv.org/abs/math/0312395]
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On the velocities of Lagrangian minimizers. Mosc. Math. J. 5:1 (2005), 157-169.
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Patterns of macroeconomic indicators preceding the unemployment rise in Western Europe and the USA. Pattern Recognition 38:3 (2005), 423-435.
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Application of optimal transport theory to reconstruction of the early Universe. In: Vershik, A. M. (Ed.), Proceedings of the L. V. Kantorovich Memorial Conference, St Petersburg, January 2004. Vol. 312 of Zapiski Nauchnykh Seminarov POMI. St Petersburg, pp. 303-309.

Back to the primordial Universe by a Monge-Ampère-Kantorovich optimization scheme. Astron. & Astrophys. 406 (2003), 393-401. [See also http://arxiv.org/abs/astro-ph/0301641]
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Reconstruction of the early Universe as a convex optimization problem. Mon. Not. R. Astron. Soc. 346:2 (2003), 501-524. [See also http://arxiv.org/abs/astro-ph/0304214]
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A reconstruction of the initial conditions of the universe by optimal mass transportation. Nature 417 (2002), 260-262. [See also http://arxiv.org/abs/astro-ph/0109483]
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Idempotent interval analysis and optimization problems. Reliab. Comput. 7:5 (2001), 353-377. [See also http://arxiv.org/abs/math/0101080]
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Idempotent mathematics and interval analysis. Comput. Tech. 6:6 (2000), 47-70. [Russian original: Литвинов Г. Л., Маслов В. П., Соболевский А. Н. Идемпотентная математика и интервальный анализ. Вычислительные технологии 6:6 (2000), 47-70; see also http://arxiv.org/abs/math/9911126]

Exact interval solutions of the discrete bellman equation, and the polynomial complexity of problems in interval idempotent linear algebra. Doklady Math. 62:2 (2000), 199-201 . [Russian original: Литвинов Г. Л., Соболевский А. Н. Точные интервальные решения дискретного уравнения Беллмана и полиномиальная сложность задач идемпотентной линейной алгебры. Доклады РАН 374:3 (2000), 304-306; see also http://arxiv.org/abs/math/0101041]
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Sobolevski, A. N. Interval arithmetic and linear algebra over idempotent semirings. Doklady Math. 369:6 (1999), 747-749. [Russian original: Соболевский А. Н. Интервальная арифметика и линейная алгебра над идемпотентными полукольцами. Доклады РАН 369:6 (1999), 747-749.]
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Sobolevski, A. N. Aubry-Mather theory and idempotent eigenfunctions of Bellman operator. Commun. Contemp. Math. 1:4 (1999), 517-533. [See also http://arxiv.org/abs/chao-dyn/9906036]
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Sobolevskii, A. N. Periodic solutions of the Hamilton-Jacobi equation with a periodic non-homogeneous term and Aubry-Mather theory. Sbornik: Math. 190:10 (1999), 1487-1504. [Russian original: Соболевский А. Н. Периодические решения уравнения Гамильтона-Якоби с периодической неоднородностью и теория Обри-Мезера. Математический сборник 190:10 (1999), 87-104.]
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Sobolevskii, A. N. Periodic solutions of the Hamilton-Jacobi equation with a periodic forcing term. Russ. Math. Surveys 53:6 (1998), 1375-1376. [Russian original: Соболевский А. Н. Периодические решения уравнения Гамильтона-Якоби с периодической силой. УМН, 53:6 (1998), 265-266; see also http://arxiv.org/abs/chao-dyn/9906035]
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Sobolevskii, A. N. The small viscosity method for a one-dimensional system of equations of gas dynamic type without pressure. Doklady Math. 56:2 (1997), 707-709. [Russian original: Соболевский А. Н. Метод исчезающей вязкости для системы уравнений типа газовой динамики без давления. Доклады РАН 356:3 (1997), 310-312.]
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