Načelo kompaktnosti i koncentracije u varijacijskom računu

Jukić, Mia (2016) Načelo kompaktnosti i koncentracije u varijacijskom računu. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

In this thesis we describe various results of concentration compactness principle and theory of interpolation. The thesis consists of four chapters. A short overview of function spaces that are to be used in later chapters is given in the first one. In the second chapter we present classical real interpolation theory with focus on the so-called K-method as well as complex interpolation theory. The functional-analytic grounds of the concentration compactness are presented in the third chapter, followed by applications on nonlinear Schrödinger equation. In the final chapter we give a formulation for the concentration compactness method in Banach space, generalizing the Hilbert case described in the previous chapter. We also give definition of cocompactness, a useful weaker counterpart of compactness. We use techniques of interpolation spaces described in the second chapter to deduce results from known cocompact imbeddings for classical Sobolev spaces.

Item Type: Thesis (Diploma thesis)
Supervisor: Antonić, Nenad
Date: 2016
Number of Pages: 47
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 25 Oct 2016 12:21
Last Modified: 25 Oct 2016 12:21
URI: http://digre.pmf.unizg.hr/id/eprint/5231

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