Data di Pubblicazione:
2017
Citazione:
On the lower semicontinuous envelope of functionals defined on polyhedral chains / M. Colombo, A. De Rosa, A. Marchese, S. Stuvard. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 163(2017), pp. 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,infinity) an even, subadditive, and lower semicontinuous function with H(0) = 0, and by Phi(H) the functional induced by H on polyhedral m-chains, namely
Phi(H) (P) := Sigma(N)(i=1) H(theta(i))H-m(sigma(i)), for every P = Sigma(N)(i=1)theta(i) [[sigma(i)]] is an element of P-m(R-n),
we prove that the lower semicontinuous envelope of Phi(H) coincides on rectifiable m-currents with the H-mass
M-H (R) := integral(E) H(theta(x)) dH(m)(x) for every R = [[E, tau, theta]] is an element of R-m(R-n).
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Rectifiable currents; H-mass; Polyhedral approximation; Relaxation
Elenco autori:
M. Colombo, A. De Rosa, A. Marchese, S. Stuvard
Link alla scheda completa: