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Specific approximation for solutions of non-linear partial differential equations

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Abstract

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

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References

  1. J. Heinonen, T. Kilpeläinen, and O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Clarendon Press, Oxford, 1993.

    MATH  Google Scholar 

  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.

  3. V. M. Miklyukov, “A-solutions with singularities as near-solutions,” Mat. Sb., 197, No. 11, 31–50 (2006).

    MathSciNet  Google Scholar 

  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.

  5. V. M. Miklyukov, Functions of Sobolev Weighted Classes, Anisotropic Metrics, and Degenerate Quasiconformal Mappings [in Russian], VolGU, Volgograd, 2010.

    Google Scholar 

  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).

  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. V. M. Miklyukov, “On the stagnation zones in superslow processes,” Dokl. Akad. Nauk, 418, No. 3, 304–307 (2008).

    Google Scholar 

  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).

    MathSciNet  Google Scholar 

  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).

    MathSciNet  Google Scholar 

  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.

  12. V. M. Miklyukov, Geometric Analysis. Differential Forms, Near-Solutions, Almost Quasiconformal Mappings, [in Russian], VolGU, Volgograd, 2007.

  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.

  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.

  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.

  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.

  17. V. M. Miklyukov, Geometric Analysis [in Russian], 2011, www.uchimsya.co.

  18. J. C. C. Nitsche, Vorlesungen über Minimalflächen, Springer, Berlin, 1975.

    MATH  Google Scholar 

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Correspondence to Vladimir M. Miklyukov.

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To R. M. Trigub in fond memory of the days of youth in DonSU

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 8, No. 4, pp. 596–606, October–November, 2011.

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Miklyukov, V.M. Specific approximation for solutions of non-linear partial differential equations. J Math Sci 182, 100–107 (2012). https://doi.org/10.1007/s10958-012-0731-5

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