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Homogenization of Variational Inequalities for the p-Laplace Operator in Perforated Media Along Manifolds

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.

 Autoría: Gómez D., Pérez E., Podolskii A., Shaposhnikova T.,

 Fuente: Applied Mathematics and Optimization, 2017, 1-19

Editorial: Springer

 Fecha de publicación: 01/11/2017

Nº de páginas: 19

Tipo de publicación: Artículo de Revista

 DOI: 10.1007/s00245-017-9453-x

ISSN: 0095-4616,1432-0606

Proyecto español: MTM2013-44883-P

Url de la publicación: https://link.springer.com/article/10.1007/s00245-017-9453-x