Relaxation of functionals with linear growth: Interactions of emerging measures and free discontinuities

0575874 - ÚTIA 2024 RIV DE eng J - Článek v odborném periodiku
Krömer, Stefan - Kružík, Martin - Zappale, E.
Relaxation of functionals with linear growth: Interactions of emerging measures and free discontinuities.
Advances in Calculus of Variations. Roč. 16, č. 4 (2023), s. 835-865. ISSN 1864-8258. E-ISSN 1864-8266
Grant CEP: GA ČR(CZ) GF19-29646L
Institucionální podpora: RVO:67985556
Klíčová slova: Lower semicontinuity * nonreflexive spaces * relaxation * concentration effects
Obor OECD: Pure mathematics
Impakt faktor: 1.7, rok: 2022
Způsob publikování: Omezený přístup
http://library.utia.cas.cz/separaty/2023/MTR/kromer-0575874-preprint.pdf https://www.degruyter.com/document/doi/10.1515/acv-2021-0063/html

For an integral functional defined on functions (u, v) ∈ W1,1 × L1 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 bring 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.
Trvalý link: https://hdl.handle.net/11104/0345850