For an integral functional defined on functions (u, v) W 1, 1 × L 1 featuring a prototypical strong interaction term between u and v, we calculate its relaxation in the space of functions with bounded variations and Radon measures. Interplay between measures and discontinuities brings various additional difficulties, and concentration effects in recovery sequences play a major role for the relaxed functional even if the limit measures are absolutely continuous with respect to the Lebesgue one.
Relaxation of functionals with linear growth: Interactions of emerging measures and free discontinuities / Kromer, S.; Kruzik, M.; Zappale, E.. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - 16:0(2023), pp. 835-865. [10.1515/acv-2021-0063]
Relaxation of functionals with linear growth: Interactions of emerging measures and free discontinuities
Zappale E.
2023
Abstract
For an integral functional defined on functions (u, v) W 1, 1 × L 1 featuring a prototypical strong interaction term between u and v, we calculate its relaxation in the space of functions with bounded variations and Radon measures. Interplay between measures and discontinuities brings various additional difficulties, and concentration effects in recovery sequences play a major role for the relaxed functional even if the limit measures are absolutely continuous with respect to the Lebesgue one.| File | Dimensione | Formato | |
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Kromer_Relaxation_2022.pdf
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