Estimates for capacity and discrepancy of convex surfaces in sieve-like domains with an application to homogenization

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Calculus of Variations and Partial Differential Equations

, 55:138

First Online: 02 November 2016Received: 26 March 2016Accepted: 05 October 2016

Abstract

We consider the intersection of a convex surface \\Gamma \ with a periodic perforation of \\mathbb {R}^d\, which looks like a sieve, given by \T \varepsilon = \bigcup {k\in \mathbb {Z}^d}\{\varepsilon k+a \varepsilon T\}\ where T is a given compact set and \a \varepsilon \ll \varepsilon \ is the size of the perforation in the \\varepsilon \-cell \0, \varepsilon ^d\subset \mathbb {R}^d\. When \\varepsilon \ tends to zero we establish uniform estimates for p-capacity, \1
Mathematics Subject Classification35R35 35B27 32U15 11K06 Communicated by F. H. Lin.

Autor: Aram L. Karakhanyan - Martin Strömqvist