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master's thesis
Primjena nelinearne funkcionalne analize u teoriji elastičnosti
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:804260
Samac, Dominik Šime
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Samac, D. Š. (2023). Primjena nelinearne funkcionalne analize u teoriji elastičnosti (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:804260

Samac, Dominik Šime. "Primjena nelinearne funkcionalne analize u teoriji elastičnosti." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:804260

Samac, Dominik Šime. "Primjena nelinearne funkcionalne analize u teoriji elastičnosti." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:804260

Samac, D. Š. (2023). 'Primjena nelinearne funkcionalne analize u teoriji elastičnosti', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:804260

Samac DŠ. Primjena nelinearne funkcionalne analize u teoriji elastičnosti [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:804260

D. Š. Samac, "Primjena nelinearne funkcionalne analize u teoriji elastičnosti", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:804260

Metadata
TitlePrimjena nelinearne funkcionalne analize u teoriji elastičnosti
Title (english)Application of nonlinear functional analysis in elasticity theory
AuthorDominik Šime Samac
MentorJosip Tambača (mentor)
Committee memberJosip Tambača (predsjednik povjerenstva)
Committee memberMatko Ljulj (član povjerenstva)
Committee memberIgor Pažanin (član povjerenstva)
Committee memberSlaven Kožić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-03-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovome radu iskazan je i dokazan John Ballov teorem o egzistenciji minimizatora određenih vrsta funkcionala. Kako bi se dokazao teorem, razvijena je teorija koja pokriva funkcionalnu analizu, s naglaskom na Banach-Saks-Mazurov teorem i Banach-Eberlein-Šmulianov teorem. Uvedeni su Soboljevljevi prostori na kojim se traže minimizatori te su dokazana osnovna svojstva Soboljevljevih prostora neophodna za dokazivanje kasnijih teorema. Prije završnih rezultata, napravljen je pregled nekih tema iz nelinearne funkcionalne analize gdje se definirala Frechetova derivacija. Naglasak tog poglavlja je na Piolinom identitetu koji se nekoliko puta iskoristio u kasnijim teoremima. Posljednje poglavlje kreće s egzistencijom minimizatora na općenitim funkcionalima. S razvijanjem teorije određene pretpostavke na funkcionale su nadodane kako bi promatrani matematički model iz teorije elastičnosti imao smisla. Naposljetku, John Ballov teorem riješi pitanje pronalaska minimizatora i za takve funkcionale.
Abstract (english)
In this paper, John Ball's theorem on the existence of minimizers of certain types of functionals is stated and proved. In order to prove the theorem, a theory covering functional analysis is developed, with an emphasis on the Banach-Saks-Mazur theorem and the Banach-Eberlein-Šmulian theorem. Sobolev spaces are introduced, on which minimizers are sought, and the basic properties of Sobolev spaces necessary for proving later theorems are proved. Before the final results, an overview of some topics from nonlinear functional analysis where the Frechet derivative was defined was made. The emphasis of that chapter is on Piola's identity, which was used several times in later theorems. The last chapter starts with the existence of minimizers on general functionals. With the development of the theory, certain assumptions were added to the functional ones in order for the observed mathematical model from the theory of elasticity to make sense. Finally, John Ball's theorem solves the problem of finding a minimizer for such functionals as well.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:804260
Study programmeTitle: Pure Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2023-08-18 09:46:39