bibtype	J - Journal Article
ARLID	0481321
utime	20240103214933.0
mtime	20171114235959.9
WOS	000414585000001
SCOPUS	85034257197
DOI	10.1137/16M1060947
title (primary) (eng)	Weak Lower Semicontinuity of Integral Functionals and Applications
specification	page_count 64 s. media_type P
serial	ARLID cav_un_epca*0255074 ISSN 0036-1445 title SIAM Review volume_id 59 volume 4 (2017) page_num 703-766
keyword	calculus of variations
keyword	weak lower semi-continuity
author (primary)	ARLID cav_un_auth*0307508 name1 Benešová name2 B. country DE
author	ARLID cav_un_auth*0101142 name1 Kružík name2 Martin full_dept (cz) Matematická teorie rozhodování full_dept Department of Decision Making Theory department (cz) MTR department MTR institution UTIA-B full_dept Department of Decision Making Theory fullinstit Ústav teorie informace a automatizace AV ČR, v. v. i.
source	url http://library.utia.cas.cz/separaty/2017/MTR/kruzik-0481321.pdf
cas_special	project ARLID cav_un_auth*0304434 project_id GA14-15264S agency GA ČR project ARLID cav_un_auth*0331681 project_id GF16-34894L agency GA ČR country CZ project ARLID cav_un_auth*0348999 project_id DAAD-16-14 agency GA AV ČR country CZ abstract (eng) Minimization is a recurring theme in many mathematical disciplines ranging from pure\nto applied. Of particular importance is the minimization of integral functionals, which is\nstudied within the calculus of variations. Proofs of the existence of minimizers usually rely\non a fine property of the functional called weak lower semicontinuity. While early stud-\nies of lower semicontinuity go back to the beginning of the 20th century, the milestones\nof the modern theory were established by C. B. Morrey, Jr. [Pacific J. Math., 2 (1952),\npp. 25–53] in 1952 and N. G. Meyers [Trans. Amer. Math. Soc., 119 (1965), pp. 125–149]\nin 1965. We recapitulate the development of this topic from these papers onwards. Spe-\ncial attention is paid to signed integrands and to applications in continuum mechanics\nof solids. In particular, we review the concept of polyconvexity and special properties of\n(sub-)determinants with respect to weak lower semicontinuity. In addition, we empha-\nsize some recent progress in lower semicontinuity of functionals along sequences satisfying\ndifferential and algebraic constraints that can be used in elasticity to ensure injectivity\nand orientation-preservation of deformations. Finally, we outline generalizations of these\nresults to more general first-order partial differential operators and make some suggestions\nfor further reading RIV BA FORD0 10000 FORD1 10100 FORD2 10101 reportyear 2018 num_of_auth 2 mrcbC52 4 A hod 4ah 20231122142810.8 inst_support RVO:67985556 permalink http://hdl.handle.net/11104/0277002 mrcbC64 1 Department of Decision Making Theory UTIA-B 10102 MATHEMATICS, APPLIED confidential S mrcbC86 1* Article Mathematics Applied mrcbC86 1* Article Mathematics Applied mrcbC86 1* Article Mathematics Applied mrcbT16-e MATHEMATICSAPPLIED mrcbT16-j 3.736 mrcbT16-s 2.273 mrcbT16-B 99.732 mrcbT16-D Q1* mrcbT16-E Q1* arlyear 2017 mrcbTft \nSoubory v repozitáři: kruzik-0481321.pdf mrcbU14 85034257197 SCOPUS mrcbU24 PUBMED mrcbU34 000414585000001 WOS mrcbU63 cav_un_epca*0255074 SIAM Review 0036-1445 1095-7200 Roč. 59 č. 4 2017 703 766