Geometric Properties of Solutions of Elliptic Variational Systems with Phase Transition Potentials and Related Minimal Surface Problems

Doctoral Dissertation uoadl:1308787 410 Read counter

Unit:
Τομέας Μαθηματικής Ανάλυσης
Library of the School of Science
Deposit date:
2016-02-12
Year:
2016
Author:
Φαλιάγκας Απόστολος
Dissertation committee:
Αλικάκος Ν., Fusco G., Καραλή Γ., Στρατής Ι., Μπαρμπάτης Γ., Παπανικολάου Β., Τερτίκας Α.
Original Title:
Γεωμετρική Μελέτη Λύσεων Ελλειπτικών Συστημάτων Μεταβολικής Δομής με Δυναμικά Αλλαγής Φάσεων και Σχετικά Προβλήματα Ελαχιστικών Επιφανειών
Languages:
Greek
Translated title:
Geometric Properties of Solutions of Elliptic Variational Systems with Phase Transition Potentials and Related Minimal Surface Problems
Summary:
The subject of this thesis is the investigation of the connectivity problem of
stable phase partitions with more than two phases by sharp interface methods,
and related variational problems. The partitioning of a set into a number of
subsets (the “phases”) so that the interface has minimal area, is a problem of
Geometric Analysis and Calculus of Variations, which is of great importance to
science and technology. From a physical point of view, we have the coexistence
of three or more phases in equilibrium, or the mechanical equilibrium of three
or more incompressible fluids, each having a given volume, in a container.
Keywords:
Elliptic Systems, Calculus of Variations, Phase Partitioning, Euler-Lagrange, Stress Tensor
Index:
No
Number of index pages:
0
Contains images:
Yes
Number of references:
159
Number of pages:
178
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