# On the lower semicontinuous envelope of functionals defined on polyhedral chains

@article{Colombo2017OnTL,
title={On the lower semicontinuous envelope of functionals defined on polyhedral chains},
author={Maria Colombo and Antonio De Rosa and Andrea Marchese and Salvatore Stuvard},
journal={Nonlinear Analysis-theory Methods \& Applications},
year={2017},
volume={163},
pages={201-215}
}
Abstract In this note we prove an explicit formula for the lower semicontinuous envelope of some functionals defined on real polyhedral chains. More precisely, denoting by H : R → [ 0 , ∞ ) an even, subadditive, and lower semicontinuous function with H ( 0 ) = 0 , and by Φ H the functional induced by H on polyhedral m -chains, namely Φ H ( P ) ≔ ∑ i = 1 N H ( θ i ) H m ( σ i ) , for every  P = ∑ i = 1 N θ i 〚 σ i 〛 ∈ P m ( R n ) , we prove that the lower semicontinuous envelope of Φ H coincides…
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