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

  • Vasilii Babich
Part of the International Mathematical Series book series (IMAT, volume 9)

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.

Keywords

Nauk SSSR Mathematical Physic Wave Equation Weak Solution Cauchy Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 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)Google Scholar
  2. 2.
    Sobolev, S.L.: The wave equation in an inhomogeneous medium (Russian). Tr. Seismol. Inst. Akad. Nauk SSSR, no. 6 (1930)Google Scholar
  3. 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)Google Scholar
  4. 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)Google Scholar
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    Sobolev, S.L.: The wave equation in an inhomogeneous medium (Russian). Tr. Seismol. Inst. Akad. Nauk SSSR, no. 16, 15–18 (1931)Google Scholar
  6. 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)Google Scholar
  7. 7.
    Smirnov, V.I., Sobolev, S.L.: Sur le problème plan des vibrations élastiques (French). C.R. Acad. Sci. Paris194, 1437–1439 (1932)MATHGoogle Scholar
  8. 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)Google Scholar
  9. 9.
    Sobolev, S.L.: On a generalization of the Kirchhoff formula (Russian, French). Dokl. Akad. Nauk SSSR1, no. 6, 256–258, 258–262 (1933)MathSciNetGoogle Scholar
  10. 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)MATHGoogle Scholar
  11. 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)Google Scholar
  12. 12.
    Sobolev, S.L.: L'équation d'onde sur la surface logarithmique de Riemann (French). C. R. Acad. Sci. Paris196, 49–51 (1933)MATHGoogle Scholar
  13. 13.
    Sobolev, S.L.: Theory of diffraction of plane waves (Russian). Tr. Seismol. Inst. Akad. Nauk SSSR, no. 41 (1934)Google Scholar
  14. 14.
    Sobolev, S.L.: On integration of the wave equation in an inhomogeneous medium (Russian). Tr. Seismol. Inst. Akad. Nauk SSSR, no. 42 (1934)Google Scholar
  15. 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)Google Scholar
  16. 16.
    Sobolev, S.L.: Functional-invariant solutions to the wave equation (Russian). Tr. Steklov Phys. Mat. Inst.5, 259–264 (1934)Google Scholar
  17. 17.
    Sobolev, S.L.: The Cauchy problem in the space of functionals (Russian, French). Dokl. Akad. Nauk SSSR3, no. 7, 291–294 (1935)Google Scholar
  18. 18.
    Sobolev, S.L.: General theory of wave diffraction on Riemannian surfaces (Russian). Tr. Steklov Mat. Inst.9, 39–105 (1935)Google Scholar
  19. 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)Google Scholar
  20. 20.
    Sobolev, S.L.: Generalized solutions to the wave equation (Russian). In: Proc. the 2nd All-Union Math. Congr. (Leningrad, 24–30 June 1934), Vol. 2, p. 259. Akad. Nauk SSSR, Moscow-Leningrad (1936)Google Scholar
  21. 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)Google Scholar
  22. 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)MathSciNetGoogle Scholar
  23. 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)Google Scholar
  24. 24.
    Sobolev, S.L.: On a theorem of functional analysis (Russian, French). Dokl. Akad. Nauk SSSR20, no. 1, 5–9 (1938)Google Scholar
  25. 25.
    Sobolev, S.L.: On the Cauchy problem for quasilinear hyperbolic equations (Russian, French). Dokl. Akad. Nauk SSSR20, no. 2–3, 79–83 (1938)MathSciNetGoogle Scholar
  26. 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)MATHGoogle Scholar
  27. 27.
    Sobolev, S.L.: On the theory of nonlinear hyperbolic partial differential equations (Russian). Mat. Sb.5, no. 1, 71–79 (1939)MATHGoogle Scholar
  28. 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)Google Scholar
  29. 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)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.St.-Petersburg Department of the Steklov Mathematical InstituteRussia

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