Generalized W1-1-Young Measures and Relaxation of Problems with Linear Growth

0487019 - ÚTIA 2019 RIV US eng J - Článek v odborném periodiku
Baia, M. - Krömer, Stefan - Kružík, Martin
Generalized W1-1-Young Measures and Relaxation of Problems with Linear Growth.
SIAM Journal on Mathematical Analysis. Roč. 50, č. 1 (2018), s. 1076-1119. ISSN 0036-1410. E-ISSN 1095-7154
Grant CEP: GA ČR GA14-15264S; GA ČR(CZ) GF16-34894L
Institucionální podpora: RVO:67985556
Klíčová slova: lower semicontinuity * quasiconvexity * Young measures
Obor OECD: Pure mathematics
Impakt faktor: 1.334, rok: 2018
http://library.utia.cas.cz/separaty/2018/MTR/kruzik-0487019.pdf

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 $\bar\Omega$.
Trvalý link: http://hdl.handle.net/11104/0282552