0481321 20240103214933.020171114235959.9 000414585000001 85034257197 10.1137/16M1060947 64 s. P cav_un_epca*02550740036-1445594 (2017)703-766 calculus of variations weak lower semi-continuity cav_un_auth*0307508 Benešová B. DE cav_un_auth*0101142 Kružík Martin Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2017/MTR/kruzik-0481321.pdf cav_un_auth*0304434 GA14-15264S GA ČR cav_un_auth*0331681 GF16-34894L GA ČR CZ cav_un_auth*0348999 DAAD-16-14 GA AV ČR CZ Minimization is a recurring theme in many mathematical disciplines ranging from pure to applied. Of particular importance is the minimization of integral functionals, which is studied within the calculus of variations. Proofs of the existence of minimizers usually rely on a fine property of the functional called weak lower semicontinuity. While early stud- ies of lower semicontinuity go back to the beginning of the 20th century, the milestones of the modern theory were established by C. B. Morrey, Jr. [Pacific J. Math., 2 (1952), pp. 25–53] in 1952 and N. G. Meyers [Trans. Amer. Math. Soc., 119 (1965), pp. 125–149] in 1965. We recapitulate the development of this topic from these papers onwards. Spe- cial attention is paid to signed integrands and to applications in continuum mechanics of solids. In particular, we review the concept of polyconvexity and special properties of (sub-)determinants with respect to weak lower semicontinuity. In addition, we empha- size some recent progress in lower semicontinuity of functionals along sequences satisfying differential and algebraic constraints that can be used in elasticity to ensure injectivity and orientation-preservation of deformations. Finally, we outline generalizations of these results to more general first-order partial differential operators and make some suggestions for further reading BA 10000 10100 10101 2018 2 4 A hod 4ah 20231122142810.8 RVO:67985556 http://hdl.handle.net/11104/0277002 1 Department of Decision Making Theory UTIA-B 10102 MATHEMATICS, APPLIED S 1* Article Mathematics Applied 1* Article Mathematics Applied 1* Article Mathematics Applied MATHEMATICS.APPLIED 5.505 2.24 15.7 0.00551 3.736 8047 2.273 4.841 25 Q1 99.732 99.8 Q1* Q1* 3.83 Q1 99.802 2017 Soubory v repozitáři: kruzik-0481321.pdf 85034257197 SCOPUS PUBMED 000414585000001 WOS cav_un_epca*0255074 SIAM Review 0036-1445 1095-7200 Roč. 59 č. 4 2017 703 766