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Galerkin Approximations in Problems with p-Laplacian

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We study the elliptic problem with p-Laplacian and construct a system of Galerkin approximations. We estimate the difference between an exact and approximate solutions in the case of constant or variable exponent p.

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References

  1. P. Lindqvist, Notes on the p-Laplace Equation, Report No. 102, University Jyv¨askylä, Jyväskylä (2006).

  2. M. D. Surnachev and V. V. Zhikov, “On existence and uniqueness classes for the Cauchy problem for parabolic equations of the p-Laplace type,” Commun. Pure Appl. Anal. 12, No. 4, 1783–1812 (2013).

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  3. V. V. Zhikov, “On variational problems and nonlinear elliptic equations with nonstandard growth condition” [in Russian]], Probl. Mat. Anal. 54, 23–112 (2011); English transl.: J. Math. Sci., New York 173, No. 5, 463-570 (2011).

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Correspondence to V. V. Zhikov.

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Translated from Problemy Matematicheskogo Analiza 85, June 2016, pp. 95-106.

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Zhikov, V.V., Yakubovich, D.A. Galerkin Approximations in Problems with p-Laplacian. J Math Sci 219, 99–111 (2016). https://doi.org/10.1007/s10958-016-3086-5

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  • DOI: https://doi.org/10.1007/s10958-016-3086-5

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