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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

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.

 Fuente: Doklady Mathematics March 2016, Volume 93, Issue 2, pp 140–144

Editorial: Maik Nauka-Interperiodica

 Fecha de publicación: 01/03/2016

Nº de páginas: 5

Tipo de publicación: Artículo de Revista

 DOI: 10.1134/S1064562416020046

ISSN: 1064-5624,1531-8362

Url de la publicación: https://link.springer.com/article/10.1134/S1064562416020046