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master's thesis
Soboljevljevi prostori
Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. urn:nbn:hr:126:956085
Vuković, Ivan
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Institutional repository: Repository of School of Applied Mathematics and Informatics

Cite this document

Vuković, I. (2024). Soboljevljevi prostori (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:956085

Vuković, Ivan. "Soboljevljevi prostori." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:956085

Vuković, Ivan. "Soboljevljevi prostori." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:956085

Vuković, I. (2024). 'Soboljevljevi prostori', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:956085

Vuković I. Soboljevljevi prostori [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:126:956085

I. Vuković, "Soboljevljevi prostori", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:126:956085

Metadata
TitleSoboljevljevi prostori
Title (english)Sobolev Spaces
AuthorIvan Vuković
MentorKrešimir Burazin (mentor)
Committee memberIvana Crnjac (predsjednik povjerenstva)
Committee memberKrešimir Burazin (član povjerenstva)
Committee memberJelena Jankov Pavlović (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-09-12, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Mathematical Analysis
Abstract
U ovom radu najprije je uveden pojam slabe derivacije te su analizirani \( L^{p}\) prostori i neka njihova svojstva, poput dualnosti, kako bi se dala podloga za proučavanje Soboljevljevih prostora koje označavamo s \( W^{m,p}\) . Soboljevljevi prostori su, jednostavno rečeno, prostori funkcija koje pripadaju prostoru \( L^{p}\), a čije slabe derivacije, do nekog reda |α| također pripadaju \( L^{p}\) prostoru. Analizirana je njihova dualnost i pokazano je da se funkcije iz tih prostora mogu aproksimirati funkcijama iz \(C^{\infty }\bigcap W^{m,p}\) te iz \(C^{\infty } \). Na kraju su analizirana ulaganja Soboljevljevih prostora u prostore neprekidnih funkcija, \( L^{p}\) prostore te konačno u same Soboljevljeve prostore.
Abstract (english)
This paper first introduces the concept of weak derivatives and then examines \( L^{p}\) spaces and their properties, such as duality, to lay the background for studying Sobolev spaces, denoted by \( W^{m,p}\). Sobolev spaces are, simply put, spaces of functions that belong to \( L^{p}\) spaces, and whose weak derivatives, up to some order |α| also belong to \( L^{p}\). The duality of these spaces is analyzed, and it is demonstrated that functions in Sobolev spaces can be approximated by functions from \(C^{\infty }\bigcap W^{m,p}\) te iz \(C^{\infty } \). Finally, the paper explores the embeddings of Sobolev spaces into spaces of continuous functions, \( L^{p}\) spaces, and eventually into Sobolev spaces themselves.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:956085
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical 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 on2024-09-23 09:40:39