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Principle of additivity in averaging of degenerate nonlinear Dirichlet problems

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Abstract

We study the problem of averaging of Dirichlet problems for degenerate nonlinear elliptic equations of the second order in domains with fine-grained boundary under the condition that the weight function belongs to a certain Muckenhoupt class. We prove a pointwise estimate for solutions of the model degenerate nonlinear problem. The averaged boundary-value problem is constructed under new structural conditions for a perforated domain. In particular, we do not assume that the diameters of cavities are small as compared with the distances between them.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    I. V. Skrypnik & D. V. Larin

Authors
  1. I. V. Skrypnik
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  2. D. V. Larin
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 1, pp. 118–135, January, 1998.

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Skrypnik, I.V., Larin, D.V. Principle of additivity in averaging of degenerate nonlinear Dirichlet problems. Ukr Math J 50, 136–154 (1998). https://doi.org/10.1007/BF02514694

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  • DOI: https://doi.org/10.1007/BF02514694

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