Elliptic Systems with Variational Structure

Postgraduate Thesis uoadl:2882475 678 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2019-10-12
Year:
2019
Author:
Gazoulis Dimitrios
Supervisors info:
Νικόλαος Αλικάκος, Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
Elliptic Systems with Variational Structure
Languages:
English
Translated title:
Elliptic Systems with Variational Structure
Summary:
In this Thesis, we study a class of variational models that have both physical and geometrical meaning. This class is Elliptic Systems of Partial Differential Equations. In chapter 1, we give a brief description of the Calculus of Variations. In chapter 2, we focus on the Elliptic System, underlying the two main mathematical tools: the Γ-convergence and the density estimate. In this chapter, our main result is two Lemmas which imply that the symmetric minimal solutions possess a free boundary. In the next chapter, we turn our attention to the mass constraint case and to a different kind of investigation. Finally, in the appendix our main result is a calculus inequality that implies a lower bound estimate for the energy functional as defined in Chapter 3.
Main subject category:
Science
Keywords:
Elliptic Systems, Calculus of Variations, Differential Equations
Index:
No
Number of index pages:
0
Contains images:
No
Number of references:
25
Number of pages:
60
Δημήτριος Γαζούλης MSc.pdf (476 KB) Open in new window