Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024539 | Nonlinear Analysis: Theory, Methods & Applications | 2017 | 15 Pages |
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:Râ[0,â) an even, subadditive, and lower semicontinuous function with H(0)=0, and by ΦH the functional induced by H on polyhedral m-chains, namely ΦH(P)ââi=1NH(θi)Hm(Ïi),for every P=âi=1NθiãÏiãâPm(Rn),we prove that the lower semicontinuous envelope of ΦH coincides on rectifiable m-currents with the H-mass MH(R)ââ«EH(θ(x))dHm(x) for every R=ãE,Ï,θãâRm(Rn).
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Authors
Maria Colombo, Antonio De Rosa, Andrea Marchese, Salvatore Stuvard,