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Homogenization of a variational inequality for the p-Laplacian in perforated media with nonlinear restrictions for the flux on the boundary of isoperimetric perforations: p equal to the dimension of the space

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Abstract

We address the homogenization of a variational inequality posed in perforated media issue from a unilateral problem for the p-Laplacian. We consider the n-Laplace operator in a perforated domain of ℝn, n ≥ 3, with restrictions for the solution and its flux (the flux associated with the n-Laplacian) on the boundary of the perforations which are assumed to be isoperimetric. The solution is assumed to be positive on the boundary of the holes and the flux is bounded from above by a negative, nonlinear monotone function multiplied by a large parameter. A certain non periodical distribution of the perforations is allowed while the assumption that their size is much smaller than the periodicity scale is performed. We make it clear that in the average constants of the problem, the perimeter of the perforations appears for any shape.

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Authors and Affiliations

  1. Universidad de Cantabria, Santander, España

    D. Gomez, M. E. Pérez & M. Lobo

  2. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    A. V. Podolsky & T. A. Shaposhnikova

Authors
  1. D. Gomez
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  2. M. E. Pérez
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  3. M. Lobo
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  4. A. V. Podolsky
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  5. T. A. Shaposhnikova
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Corresponding author

Correspondence to D. Gomez.

Additional information

Published in Russian in Doklady Akademii Nauk, 2016, Vol. 467, No. 1, pp. 18–22.

The article was translated by the authors.

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Gomez, D., Pérez, M.E., Lobo, M. et al. Homogenization of a variational inequality for the p-Laplacian in perforated media with nonlinear restrictions for the flux on the boundary of isoperimetric perforations: p equal to the dimension of the space. Dokl. Math. 93, 140–144 (2016). https://doi.org/10.1134/S1064562416020046

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  • DOI: https://doi.org/10.1134/S1064562416020046

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