Siberian Mathematical Journal

, Volume 13, Issue 4, pp 533–545 | Cite as

The maximum principle for an elliptic — Parabolic equation of the second order

  • L. I. Kamynin
  • B. N. Khimchenko
Article

Keywords

Maximum Principle Parabolic Equation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    O. A. Oleinik, “On the properties of the solutions of some boundary problems for equations of elliptic type,” Matem. Sb.,30, (3), 695–702 (1952).Google Scholar
  2. 2.
    E. Hopf, “A remark on linear elliptic differential equations of the second order,” Proc. Amer. Math. Soc.,3, 791–793 (1952).Google Scholar
  3. 3.
    B. N. Khimchenko, “On the behavior of the solutions of an elliptic equation close to a boundary of type A(1),” Candidate's Dissertation [in Russian], In-ta Prikl. Matem., AN SSSR, Moscow (1970).Google Scholar
  4. 4.
    R. Byborny, “On the properties of the solutions of some boundary problems for equations of parabolic type,” Dokl. Akad. Nauk SSSR,117, No. 3, 563–565 (1957).Google Scholar
  5. 5.
    A. Friedman, “Remarks on the maximum principle for parabolic equations and its applications,” Pacific J. Math.,8, 201–211 (1958).Google Scholar
  6. 6.
    A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, New Jersey (1964).Google Scholar
  7. 7.
    L. I. Kamynin and B. N. Khimchenko, “On the maximum principle for parabolic equations of the second order,” Dokl. Akad. Nauk SSSR,200, No. 2, 282–285 (1971).Google Scholar
  8. 8.
    A. F. Timan, Theory of Approximations of Functions of a Real Variable, Macmillan, New York (1963).Google Scholar
  9. 9.
    L. Nirenberg, “A strong maximum principle for parabolic equations,” Comm. Pure Appl. Math.,6, 167–177 (1953).Google Scholar
  10. 10.
    G. Girand, “Generalisation des problemes sur les operations du type elliptique,” Bull. Sci. Math.,60, 316–352 (1932).Google Scholar
  11. 11.
    G. Girand, “Problemes de valeurs a la frontiere relatifs a certaines donnees discontinues,” Bull. Soc. Math. France,61, 1–54 (1933).Google Scholar
  12. 12.
    M. V. Keldysh and M. A. Lavrent'ev, “On the uniqueness of the Neumann problem,” Dokl. Akad. Nauk SSSR,16, 151–152 (1937).Google Scholar
  13. 13.
    G. M. Verzhbinskii and V. G. Maz'ya, “On the asymptotics of the solutions of Dirichlet's problem close to a nonregular boundary,” Dokl. Akad. Nauk SSSR,176, No. 3, 498–501 (1967).Google Scholar
  14. 14.
    N. V. Efimov and É. R. Rozendorn, Linear Algebra and Multidimensional Geometry [in Russian], Nauka (1970).Google Scholar
  15. 15.
    R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 1, Interscience, New York (1957).Google Scholar

Copyright information

© Consultants Bureau, a division of Plenum Publishing Corporation 1973

Authors and Affiliations

  • L. I. Kamynin
  • B. N. Khimchenko

There are no affiliations available

Personalised recommendations