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
- Authors: Gomez D.1, Pérez M.E.1, Lobo M.1, Podolsky A.V.2, Shaposhnikova T.A.2
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Affiliations:
- Universidad de Cantabria
- Faculty of Mechanics and Mathematics
- Issue: Vol 93, No 2 (2016)
- Pages: 140-144
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/223453
- DOI: https://doi.org/10.1134/S1064562416020046
- ID: 223453
Cite item
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.
About the authors
D. Gomez
Universidad de Cantabria
Author for correspondence.
Email: gomezdel@unican.es
Spain, Santander
M. E. Pérez
Universidad de Cantabria
Email: gomezdel@unican.es
Spain, Santander
M. Lobo
Universidad de Cantabria
Email: gomezdel@unican.es
Spain, Santander
A. V. Podolsky
Faculty of Mechanics and Mathematics
Email: gomezdel@unican.es
Russian Federation, Moscow, 119991
T. A. Shaposhnikova
Faculty of Mechanics and Mathematics
Email: gomezdel@unican.es
Russian Federation, Moscow, 119991