Relaxation and Gamma-convergence of supremal functionals
نویسنده
چکیده
Sunto. Si prova che il Γ-limite in Lμ di una successione di funzionali supremali della forma Fk(u) = μ-ess supΩ fk(x, u) é un funzionale supremale. In un controesempio si mostra che la funzione che rappresenta il Γ-limite F (·, B) di una successione di funzionali supremali della forma Fk(u,B) = μ-ess supB fk(x, u) puó dipendere dall’insieme B e si stabilisce una condizione necessaria e sufficiente al fine di rappresentare F nella forma supremale F (u,B) = μ-ess supB f(x, u). Come corollario, si dimostra che se f rappresenta un funzionale supremale F , allora l’inviluppo level convex di f rappresenta l’inviluppo semicontinuo inferiormente di F rispetto alla topologia debole* di Lμ .
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