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On the Mathematical Works of S.L. Sobolev in the 1930s

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Sobolev Spaces in Mathematics II

Part of the book series: International Mathematical Series ((IMAT,volume 9))

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Abstract

A review of the works of S.L. Sobolev that have played a funda mental role in the development of the theory of partial differential equations and mathematical analysis in the second part of the 20th century. Supplied with a short biographical note.

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References

  1. Sobolev, S.L.: Remarks on the works of N.N. Saltykov “Research in the theory of first order partial differential equations with one unknown function” and “On the development of the theory of first order partial differential equations with one unknown function” (Russian). Dokl. Akad. Nauk SSSR, no.7, 168–170 (1929)

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  2. Sobolev, S.L.: The wave equation in an inhomogeneous medium (Russian). Tr. Seismol. Inst. Akad. Nauk SSSR, no. 6 (1930)

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  3. Sobolev, S.L.: Sur l'équation d'onde pour le cas d'un milieu hétérogène isotrope (French). Dokl. Akad. Nauk SSSR, no.7, 163–167 (1930)

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  4. Smirnov, V.I., Sobolev S.L.: On a new method for solving the plane problem of elastic oscillations (Russian). Tr. Seismol. Inst. Akad. Nauk SSSR, no. 16, 14–15 (1931)

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  5. Sobolev, S.L.: The wave equation in an inhomogeneous medium (Russian). Tr. Seismol. Inst. Akad. Nauk SSSR, no. 16, 15–18 (1931)

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  6. Smirnov, V.I., Sobolev, S.L.: Sur une méthode nouvelle dans le problème plan des vibrations élastiques (French). Tr. Seismol. Inst. Akad. Nauk SSSR, no. 18 (1932)

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  7. Smirnov, V.I., Sobolev, S.L.: Sur le problème plan des vibrations élastiques (French). C.R. Acad. Sci. Paris194, 1437–1439 (1932)

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  8. Smirnov, V.I., Sobolev, S.L.: Sur l'application de la méthode nouvelle a l'étude des vibrations élastiques dans l'espace `a symmetrie axiale (French). Tr. Seismol. Inst. Akad. Nauk SSSR, no. 29 (1933)

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  9. Sobolev, S.L.: On a generalization of the Kirchhoff formula (Russian, French). Dokl. Akad. Nauk SSSR1, no. 6, 256–258, 258–262 (1933)

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  10. Sobolev, S.L.: On vibration of a half-plane and of a lamina under arbitrary initial conditions (French). Mat. Sb.40, no. 2, 236–266 (1933); English transl.: Russ. Math. Surv.23, no. 5, 95–129 (1968)

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  11. Sobolev, S.L.: On a method for solving the problem of oscillation propagation (Rus sian). Prikl. Mat. Mekh.1, no. 2, 290–309 (1933)

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  12. Sobolev, S.L.: L'équation d'onde sur la surface logarithmique de Riemann (French). C. R. Acad. Sci. Paris196, 49–51 (1933)

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  13. Sobolev, S.L.: Theory of diffraction of plane waves (Russian). Tr. Seismol. Inst. Akad. Nauk SSSR, no. 41 (1934)

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  14. Sobolev, S.L.: On integration of the wave equation in an inhomogeneous medium (Russian). Tr. Seismol. Inst. Akad. Nauk SSSR, no. 42 (1934)

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  15. Sobolev, S.L.: A new method for solving the Cauchy problem for partial differential equations of second order (Russian, French). Dokl. Akad. Nauk SSSR1, no. 8, 433–435, 435–438 (1934)

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  16. Sobolev, S.L.: Functional-invariant solutions to the wave equation (Russian). Tr. Steklov Phys. Mat. Inst.5, 259–264 (1934)

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  17. Sobolev, S.L.: The Cauchy problem in the space of functionals (Russian, French). Dokl. Akad. Nauk SSSR3, no. 7, 291–294 (1935)

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  18. Sobolev, S.L.: General theory of wave diffraction on Riemannian surfaces (Russian). Tr. Steklov Mat. Inst.9, 39–105 (1935)

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  19. Sobolev, S.L.: A new method for solving the Cauchy problem for partial differential equations of hyperbolic type (Russian). In: Proc. the 2nd All-Union Math. Congr. (Leningrad, 24–30 June 1934), Vol. 2, pp. 258–259. Akad. Nauk SSSR, Moscow— Leningrad (1936)

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  21. Sobolev, S.L.: On the diffraction problem on Riemannian surfaces (Russian). In: Proc. the 2nd All-Union Math. Congr. (Leningrad, 24–30 June 1934), Vol. 2, p. 364. Akad. Nauk SSSR, Moscow-Leningrad (1936)

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  22. Sobolev, S.L.: The Schwarz algorithm in the theory of elasticity (Russian, French). Dokl. Akad. Nauk SSSR4, no. 6, 235–238, 243–246 (1936)

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  23. Sobolev, S.L.: Méthode nouvelle à résoudre le problème de Cauchy pour les équations linéaires hyperboliques normales (French). Mat. Sb.1, no. 1, 39–72 (1936); English transl.: In: Sobolev, S.L.: Some Applications of Functinal Analysis in Mathematical Physics. Third edition. Appendix. Am. Math. Soc., Providence, RI (1991)

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  24. Sobolev, S.L.: On a theorem of functional analysis (Russian, French). Dokl. Akad. Nauk SSSR20, no. 1, 5–9 (1938)

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  25. Sobolev, S.L.: On the Cauchy problem for quasilinear hyperbolic equations (Russian, French). Dokl. Akad. Nauk SSSR20, no. 2–3, 79–83 (1938)

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  26. Sobolev, S.L.: On a theorem of functional analysis (Russian). Mat. Sb.4, no. 3, 471– 496 (1938); English transl.: In: Eleven Papers in Analysis. Am. Math. Soc. Transl. (2)34, 39–68 (1963)

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  27. Sobolev, S.L.: On the theory of nonlinear hyperbolic partial differential equations (Russian). Mat. Sb.5, no. 1, 71–79 (1939)

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  28. Sobolev, S.L.: On the stability of solutions to boundary value problems for partial differential equations of hyperbolic type (Russian, French). Dokl. Akad. Nauk SSSR32, no. 7, 459–462 (1941)

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  29. Sobolev, S.L.: Some Applications of Functional Analysis in Mathematical Physics (Russian). 1st ed. Leningrad State Univ., Leningrad (1950); 2nd ed. SB Akad. Nauk SSSR, Novosibirsk (1962); 3rd ed. Nauka, Moscow (1988); English transl. of the first edition: Am. Math. Soc., Providence, RI (1963); English transl. of the third edition, with Appendix (English transl. of the paper [23] by S.L. Sobolev) and comments on the appendix by V.P. Palamodov: Am. Math. Soc., Providence, RI (1991)

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Authors and Affiliations

  1. St.-Petersburg Department of the Steklov Mathematical Institute, 27 Fontanka, St. Petersburg 191023, Russia

    Vasilii Babich

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  1. Vasilii Babich
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Correspondence to Vasilii Babich .

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Editors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, USA

    Vladimir Maz'ya

  2. Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

    Vladimir Maz'ya

  3. Department of Mathematics, Linköping University, Linköping, Sweden

    Vladimir Maz'ya

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Babich, V. (2009). On the Mathematical Works of S.L. Sobolev in the 1930s. In: Maz'ya, V. (eds) Sobolev Spaces in Mathematics II. International Mathematical Series, vol 9. Springer, New York, NY. https://doi.org/10.1007/978-0-387-85650-6_1

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