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

0575874 - ÚTIA 2024 RIV DE eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GF19-29646L
Institutional support: RVO:67985556
Keywords : Lower semicontinuity * nonreflexive spaces * relaxation * concentration effects
OECD category: Pure mathematics
Impact factor: 1.7, year: 2022
Method of publishing: Limited access
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.
Permanent Link: https://hdl.handle.net/11104/0345850