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Journal of Mathematical Sciences

, Volume 182, Issue 1, pp 100–107 | Cite as

Specific approximation for solutions of non-linear partial differential equations

  • Vladimir M. Miklyukov
Article
  • 43 Downloads

Abstract

The concept of the almost-solution of a partial differential equation is introduced and considered.

Keywords

Generalized solution almost-solution 

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References

  1. 1.
    J. Heinonen, T. Kilpeläinen, and O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Clarendon Press, Oxford, 1993.MATHGoogle Scholar
  2. 2.
    V. M. Miklyukov, “A special approximation of solutions of partial differential equations,” in Abstracts of the International Conference in Modern Analysis [in Russian], Donetsk National University, Donetsk, June 20–23, 2011, p. 78.Google Scholar
  3. 3.
    V. M. Miklyukov, “A-solutions with singularities as near-solutions,” Mat. Sb., 197, No. 11, 31–50 (2006).MathSciNetGoogle Scholar
  4. 4.
    V. M. Miklyukov, “Almost quasiconformal mappings as near-solutions,” in Mathematical and Applied Analysis [in Russian], Iss. 3, Tyumen Univ., Tyumen, 2007, 59–70.Google Scholar
  5. 5.
    V. M. Miklyukov, Functions of Sobolev Weighted Classes, Anisotropic Metrics, and Degenerate Quasiconformal Mappings [in Russian], VolGU, Volgograd, 2010.Google Scholar
  6. 6.
    V. M. Miklyukov, “The principle of maximum for the difference of the near-solutions of nonlinear elliptic equations,” Vest. Tomsk. Gos. Univ. Mat. Mekh., No. 1, 33–45 (2007).Google Scholar
  7. 7.
    V. M. Miklyukov, “The stagnation zones of the solutions and near-solutions of elliptic equations,” Trudy Mat. Tsentra im. N. I. Lobachevskogo, 35, 174–181 (2007).Google Scholar
  8. 8.
    V. M. Miklyukov, “On the stagnation zones in superslow processes,” Dokl. Akad. Nauk, 418, No. 3, 304–307 (2008).Google Scholar
  9. 9.
    V. M. Miklyukov, “Estimates of the size of the stagnation zone for the near-solutions of equations of the parabolic type,” Sib. Zh. Indust. Mat., XI, No. 3, 96–101 (2008).MathSciNetGoogle Scholar
  10. 10.
    V. M. Miklyukov, “To the Harnack inequality for the near-solutions of elliptic equations,” Izv. RAN, Ser. Mat., 73, No. 5, 171–180 (2009).MathSciNetGoogle Scholar
  11. 11.
    V. M. Miklyukov, “Solutions of parabolic equations as the near-solutions of elliptic ones,” in Mathematical and Applied Analysis [in Russian], Iss. 4, Tyumen Univ., Tyumen, 2010, 96–113.Google Scholar
  12. 12.
    V. M. Miklyukov, Geometric Analysis. Differential Forms, Near-Solutions, Almost Quasiconformal Mappings, [in Russian], VolGU, Volgograd, 2007.Google Scholar
  13. 13.
    V. M. Miklyukov, “The theorem on three spheres for almost harmonic functions,” in Proceed. of Seminar “Superslow processes”, Iss. 5, [in Russian], VolGU, Volgograd, 2010, 15–24.Google Scholar
  14. 14.
    V. M. Miklyukov, “The theorem on two spheres for the near-solutions of equations like the minimal surface equation,” in Proceed. of Seminar “Superslow processes”, Iss. 5, [in Russian], VolGU, Volgograd, 2010, 52–62.Google Scholar
  15. 15.
    V. M. Miklyukov, “The Liouville theorem for the near-solutions of A-harmonic equations,” in Proceed. of Seminar “Superslow processes”, Iss. 5, [in Russian], VolGU, Volgograd, 2010, 162–174.Google Scholar
  16. 16.
    V. M. Miklyukov, “The Liouville theorem for almost closed differential forms of special classes,” in Proceed. of Seminar “Superslow processes”, Iss. 5, [in Russian], VolGU, Volgograd, 2010, 181–187.Google Scholar
  17. 17.
    V. M. Miklyukov, Geometric Analysis [in Russian], 2011, www.uchimsya.co.
  18. 18.
    J. C. C. Nitsche, Vorlesungen über Minimalflächen, Springer, Berlin, 1975.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.Independent Scientific Laboratory “Uchimsya.LLC”New YorkUSA

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