20.500.12556/RUL-151929 Closure result for $\Gamma$-limits of functionals with linear growth We consider integral functionals $F_\epsilon^{(j)}$, doubly indexed by $\epsilon$ > 0 and $j \in \mathbb{N} \cup \{\infty\}$, satisfying a standard linear growth condition. We investigate the question of $\Gamma$-closure, i.e., when the $\Gamma$-convergence of all families $\{F_\epsilon^{(j)}\}_ε$ with finite $j$ implies $\Gamma$-convergence of $\{F_\epsilon^{(\infty)}\}_ε$. This has already been explored for $p$-growth with $p$ > 1. We show by an explicit counterexample that due to the differences between the spaces $W^{1,1}$ and $W^{1,p}$ with $p$ > 1, an analog cannot hold. Moreover, we find a sufficient condition for a positive answer. $\Gamma$-convergence $\Gamma$-closure results functionals with standard linear growth gama konvergenca gama zaprtje funkcionali s standardno linearno rastjo true false true Angleški jezik Slovenski jezik Članek v reviji 2023-10-25 15:56:33 2023-10-25 15:56:34 2024-09-30 09:32:25 0000-00-00 00:00:00 2023 0 0 Str. 2333–2343 iss. 5 Vol. 202 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517 0373-3114 10.1007/s10231-023-01322-1 153548803 s10231-023-01322-1.pdf s10231-023-01322-1.pdf 1 4739868604D12500EBE084ABD7AE6201 cdf4b66d3d9e1099b6b8b0fa1ef68b7ac88b406bf76973ab09e0b8004ee532fc a9817024-733e-11ee-91a5-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=177084 https://link.springer.com/article/10.1007/s10231-023-01322-1 1 4fe52e00-733e-11ee-91a5-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=177083 Fakulteta za gradbeništvo in geodezijo 0 0 0