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Relaxation and Γ-convergence of quadratic forms inBV(I; ℝn)

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Si studia l’inviluppo semicontinuo inferiore e il Γ-limite di funzionali integrali quadratici degeneri, sullo spazio delle funzioni vettoriali di variazione limitata definite su un intervallo. Si dà una formula di rappresentazione integrale che dipende da una nuova matrice «rilassata» e da alcuni vincoli lineari sulla misura derivata.

Abstract

We study the lower semicontinuous envelope and the Γ-limit of degenerate quadratic integral functionals, on the space of the vector-valued functions of bounded variation defined on an interval, which are still quadratic integral functionals. We give an integral representation formula involving a new «relaxed» matrix and some linear contraints on the derivative measure.

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Author notes

  1. Andrea Braides

    Present address: Dipartimento di Elettronica per l’Automazione, Università di Brescia, via Valotti 9, I-25060, Brescia

  2. Virginia De Cicco

    Present address: S.I.S.S.A., via Beirut 2-4, I-34014, Trieste

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    1. Andrea Braides
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    2. Virginia De Cicco
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    Braides, A., De Cicco, V. Relaxation and Γ-convergence of quadratic forms inBV(I; ℝn). Ann. Univ. Ferrara 38, 145–175 (1992). https://doi.org/10.1007/BF02827089

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