An overview of some works of S.L. Sobolev

References

• Sobolev SL. Wave equation for an inhomogeneous medium. Transactions of the Seismological Institute of the USSR Academy of Sciences. Leningrad: Publishing House of the USSR Academy of Sciences; 1930. No. 6. 57 p. (Russian).
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• Hadamard J. Lectures on Cauchy's problem in linear partial differential equations. New Haven: Yale University Press; 1923. (English).
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• Smirnov VI. Course of higher mathematics. Vol. 4, part 2. Moscow: Nauka; 1981. (Russian).
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• Sobolev SL. Application of the theory of plane waves to the Lamb problem. Transactions of the Seismological Institute of the USSR Academy of Sciences. Leningrad: Publishing House of the USSR Academy of Sciences; 1932. No. 18. 41 p. (Russian).
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• Smirnov V, Sobolev S. Sur une méthode nouvelle dans le problème plan des vibrations élastiques. Transactions of the Seismological Institute of the USSR Academy of Sciences. Leningrad: Publishing House of the USSR Academy of Sciences; 1932. No. 20. 37 p. (French).
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• Smirnov V, Sobolev S. Sur l'application de la méthode nouvelle à l'étude des vibrations élastiques dans l'espace à symétrie axiale. Transactions of the Seismological Institute of the USSR Academy of Sciences. Leningrad: Publishing House of the USSR Academy of Sciences; 1933. No. 29. 49 p. (French).
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• Sobolev SL. Functionally invariant solutions of the wave equation. Tr Fiz-Mat Inst Steklova. 1934;5:259–264. (Russian).
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• Sobolev SL. On a new method of solving problems about propagation of vibrations. Prikl Mat Mekh. 1933;1(2):290–309. (Russian).
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• Soboleff S. Sur les vibrations d'un demiplan et d'une couche à conditions initiales arbitraires. Mat Sb. 1933;40(2):236–265. (French).
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• Sobolev SL. Theory of plane wave diffraction. Transactions of the Seismological Institute of the USSR Academy of Sciences. Leningrad: Publishing House of the USSR Academy of Sciences; 1934. No. 41. 23 p. (Russian).
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• Bulletin of the the Second All-Union Mathematical Congress; Leningrad; 1934. (Russian).
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• Sobolev SL. To the question on the integration of the wave equation in an inhomogeneous medium. Transactions of the Seismological Institute of the USSR Academy of Sciences. Leningrad: Publishing House of the USSR Academy of Sciences; 1934. No. 42. 26 p. (Russian).
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• Sobolev SL. A new method for solving the Cauchy problem for partial differential equations of second order. Dokl Akad Nauk SSSR. 1934;1(8):433–435. (Russian). Transl.: Nouvelle méthode de résolution du problème de Cauchy pour les équations aux dérivées partielles de second ordre. C R (Dokl) Acad Sci URSS. 1934;1(8):435–438 (French).
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• Sobolev SL. General theory of diffraction of waves on Riemann surfaces. Tr Mat Inst Steklova. 1935;9:39–105. (Russian).
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• Sobolev SL. The Cauchy problem in the space of functionals. Dokl Akad Nauk SSSR. 1935;3(7):291–294. (Russian).
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• Soboleff S. Méthode nouvelle à résoudre le problème de Cauchy pour les équations linéaires hyperboliques normales. Mat Sb. 1936;43(1):39–72. (French).
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• Schwartz L. Théorie des distributions. Tome I. Paris: Hermann & Cie; 1950. Théorie des distributions. Tome II. Paris: Hermann & Cie; 1951. (French).
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• Leray J. A reference to the works of S. L. Sobolev during the years 1930–1955 (note of A. P. Yushkevich). Istor-Mat Issled (Histor Math Res). 1993;34:267–273. (Russian).
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• Sobolev SL. On a boundary value problem for polyharmonic equations. Mat Sb. 1937;2(3):465–499. (Russian). Transl.: Am Math Soc.; Transl.: II. Ser. 1963;33:1–40. (English).
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• Sobolev SL. On a theorem of functional analysis. Mat Sb. 1938;4(3):471–497. (Russian). Transl.: Am Math Soc.; Transl.: II. Ser. 1963;34:39–68. (English).
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• Sobolev SL. To the theory of nonlinear hyperbolic partial differential equations. Mat Sb. 1939;5(1):71–99. (Russian).
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• Sobolev SL. On a class of integro-differential equations for several independent variables. Part I. Izv Akad Nauk SSSR Ser Mat. 1937;1(4):515–549. (Russian).
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• Sobolev SL. On a class of integro-differential equations with several independent variables. Part II. Izv Akad Nauk SSSR Ser Mat. 1938;2(1):61–90. (Russian).
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• Sobolev SL. Some new problems in the theory of partial differential equations of hyperbolic type. Mat Sb. 1942;11(3):155–203. (Russian).
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• Sobolev SL. On the almost periodicity of solutions to the wave equation. I. Dokl Akad Nauk SSSR. 1945;48(8):570–573. (Russian).
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• Sobolev SL. On the almost periodicity of solutions to the wave equation. II. Dokl Akad Nauk SSSR. 1945;48(9):646–648. (Russian).
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• Sobolev SL. On the almost periodicity of solutions to the wave equation. III. Dokl Akad Nauk SSSR. 1945;49(1):12–15. (Russian).
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• Sobolev SL. Some applications of functional analysis in mathematical physics. Leningrad: Izdat. Leningrad. Gos. Univ.; 1950. (Russian). Transl.: Applications of functional analysis in mathematical physics. Providence: American Mathematical Society (AMS); 1963. (Translations of mathematical monographs; vol. 7). (English). – 2nd ed., rev. and compl. Novosibirsk: Izdat. Novosibirsk. Gos. Univ.; 1962. (Russian). Transl.: Einige Anwendungen der Funktionalanalysis auf Gleichungen der mathematischen Physik. Berlin: Akademie-Verlag; 1964. (German). – 3rd ed., rev. and compl. Moscow: Nauka; 1988. (Russian). Transl.: Providence: American Mathematical Society (AMS); 1991 (Translations of mathematical monographs; vol. 90). (English).
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• Sobolev SL. On a new problem of mathematical physics. Izv Akad Nauk SSSR Ser Mat. 1954;18(1):3–50. (Russian).
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• Poincaré H. Sur l'équilibre d'une masse fluide animée d'un mouvement de rotation. Acta Math. 1885;7:259–380. (French).
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• Sobolev SL. On motion of a symmetric top with a cavity filled with fluid. Zh Prikl Mekh Tekh Fiz. 1960;1(3):20–55. (Russian).
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• Oleinik OA. I. G. Petrovskii and modern mathematics. In: Petrovskii IG, editor. Selected works. Systems of partial differential equations. Algebraic geometry. Moscow: Nauka; 1986. P. 7–33. (Russian).
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• Demidenko GV, Uspenskii SV. Partial differential equations and systems not solvable with respect to the highest-order derivative. Novosibirsk: Nauchnaya Kniga; 1998. (Russian). Transl.: New York, Basel: Marcel Dekker; 2003. (Pure and applied mathematics; vol. 256). (English).
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• Sveshnikov AG, Al'shin AB, Korpusov MO, et al. Linear and nonlinear equations of Sobolev type. Moscow: Fizmatlit; 2007. (Russian).
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• Sobolev SL. Introduction to the theory of cubature formulas. Moscow: Nauka; 1974. (Russian). Transl.: [abridged version]: Cubature formulas and modern analysis: An introduction. Montreux: Gordon and Breach Science Publishers; 1992. (English).
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• Sobolev SL. Selected questions of the theory of functional spaces and generalized functions. Edited by S. V. Uspenskii. Moscow: Nauka; 1989. (Russian).
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• Sobolev SL, Vaskevich VL. Cubature formulas. Novosibirsk: Izdatel'stvo Instituta Matematiki; 1996. (Russian). Transl.: The theory of cubature formulas. Dordrecht: Kluwer Academic Publishers; 1997. (Mathematics and its applications; vol. 415). (English).
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• Sobolev SL. Selected works. Vol. I. Equations of mathematical physics. Computational mathematics and cubature formulas. Compiled and edited by V. L. Vaskevich and G. V. Demidenko. Novosibirsk: Izdatel'stvo Instituta Matematiki, Filial “Geo” Izdatel'stva SO RAN; 2003. (Russian). Transl.: Selected works of S. L. Sobolev. Volume I: Equations of mathematical physics, computational mathematics, and cubature formulas. Edited by G. V. Demidenko and V. L. Vaskevich. New York: Springer; 2006. (English).
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• Sobolev SL. Selected works. Vol. II. Functional analysis. Partial differential equations. Compiled and edited by G. V. Demidenko and S. K. Vodop'yanov. Novosibirsk: Izdatel'stvo Instituta Matematiki, Akademicheskoe Izdatel'stvo “Geo”; 2006. (Russian).
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• Soboleva TS, Chechkin GA. Sergei L'vovich Sobolev. Facets of talent (Great mathematicians of the 20th century). Moscow: KURS; 2017. (Russian).
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• Sergei L'vovich Sobolev (1908–1989). Biobibliographic index. Compiled by V. M. Pestunova, ed. and with an introduction by S. S. Kutateladze. 4th ed., rev. and compl. Novosibirsk: Izdatel'stvo Instituta Matematiki; 2013. (Russian, English).
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• Sergei L'vovich Sobolev. Available from: http://www.math.nsc.ru/conference/sobolev/english/About_Sobolev_SL.htm.
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• Conferences dedicated to Sergei L'vovich Sobolev. Available from: http://www.math.nsc.ru/conference/sobolev/english/index.htm.
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