English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We address homogenization problems of variational inequalities for the p-Laplace operator in a domain of \(\mathbb {R}^n\) (\(n\ge \) 3, \(p\in [2,n)\)) periodically perforated by balls of radius \(O(\varepsilon ^\alpha )\) where \(\alpha >1\) and \(\varepsilon \) is the size of the period. The perforations are distributed along a \((n-1)\)-dimensional manifold \(\gamma \), 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 \(\varepsilon ^{-\kappa }\), \(\kappa \in \mathbb {R}\) and \(\varepsilon \) is a small parameter that we shall make to go to zero. We analyze different relations between the parameters \(p, \, n, \, \varepsilon , \, \alpha \) and \(\kappa \), and obtain homogenized problems which are completely new in the literature even for the case \(p=2\).

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