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/

Global: Zendy Tools annual

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

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This work adresses the question of density of piecewise constant (resp.rigid) functions in the space of vector valued functions with bounded variation(resp. deformation) with respect to the strict convergence. Such anapproximation property cannot hold when considering the usual total variationin the space of measures associated to the standard Frobenius norm in the spaceof matrices. It turns out that oscillation and concentration phenomena interactin such a way that the Frobenius norm has to be homogenized into a (resp.symmetric) Schatten-1 norm which coincides with the Euclidean norm on rank-one(resp. symmetric) matrices. By means of explicit constructions consisting ofthe superposition of sequential laminates, the validity of an optimalapproximation property is established at the expense of endowing the space ofmeasures with a total variation associated with the homogenized norm in thespace of matrices.

Piecewise rank-one approximation of vector fields with measure derivatives