0487019 20240103215642.720180221235959.9 85043500334 000426630900034 10.1137/16M1103464 44 s. P cav_un_epca*02575970036-1410501 (2018)1076-1119SIAM Society for Industrial and Applied Mathematics lower semicontinuity quasiconvexity Young measures cav_un_auth*0359167 Baia M. PT cav_un_auth*0359168 Krömer Stefan UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory DE Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101142 Kružík Martin UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2018/MTR/kruzik-0487019.pdf cav_un_auth*0304434 GA14-15264S GA ČR cav_un_auth*0331681 GF16-34894L GA ČR CZ In this work we completely characterize generalized Young measures generated by sequences of gradients of maps in $W^{1,1}(\Omega-{R}^M)$, where $\Omega\subset{R}^N$. This characterization extends and completes previous analysis by Kristensen and Rindler [Arch. Ration. Mech. Anal., 197 (2010), pp. 539--598 and 203 (2012), pp. 693--700] where concentrations of the sequence of gradients at the boundary of $\Omega$ were excluded. As an application of our result we study the relaxation of non-quasiconvex variational problems with linear growth at infinity, and, finally, we link our characterization to Souček spaces [J. Souček, Časopis Pro Pěstování Matematiky, 97 (1972), pp. 10--46], an extension of $W^{1,1}(\Omega-{\mathbb{R}}^M)$ where gradients are considered as measures on $\bar\Omega$. BA 10000 10100 10101 2019 3 4 A hod 4ah 20231122143037.9 RVO:67985556 http://hdl.handle.net/11104/0282552 1 Department of Decision Making Theory UTIA-B 10102 MATHEMATICS, APPLIED S 2 Article Mathematics Applied MATHEMATICS.APPLIED 1.845 0.28 13.2 0.0151 1.525 6078 2.396 1.235 200 Q2 91.304 63.6 Q1* Q1* 1.07 Q2 63.583 2018 Soubory v repozitáři: kruzik-0487019.pdf 85043500334 SCOPUS PUBMED 000426630900034 WOS cav_un_epca*0257597 SIAM Journal on Mathematical Analysis 0036-1410 1095-7154 Roč. 50 č. 1 2018 1076 1119 SIAM Society for Industrial and Applied Mathematics