Homogenization of Variational Inequalities for the p-Laplace Operator in Perforated Media Along Manifolds
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Gómez Gandarillas, Delfina; Pérez Martínez, María Eugenia; Podolskii, A. V.; Shaposhnikova, T. A.Fecha
2017-11Derechos
© Springer. This is a post-peer-review, pre-copyedit version of an article published in Applied Mathematics and Optimization. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00245-017-9453-x
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Applied Mathematics & Optimization 2017, 1-19
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Springer
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Resumen/Abstract
We address homogenization problems of variational inequalities for the p-Laplace operator in a domain of Rn (n ? 3, p ? [2, n)) periodically perforated by balls of radius O(??) where ? > 1 and ? is the size of the period. The perforations are distributed along a (n ? 1)-dimensional manifold ? , and we impose constraints for solutions and their fluxes (associated with the p-Laplacian) on the boundary of the perforations. These constraints imply that the solution is positive and that the flux is bounded from above by a negative, nonlinear monotonic function of the solution multiplied by a parameter ? ?? , ? ? R and ? is a small parameter that we shall make to go to zero. We analyze different relations between the parameters p, n, ?, ? and ?, and obtain homogenized problems which are completely new in the literature even for the case p = 2.
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