Unit:
Τομέας Μαθηματικής ΑνάλυσηςLibrary of the School of Science
Author:
Αντωνόπουλος Παναγιώτης
Supervisors info:
Αλικάκος Νικόλαος Καθηγ. (Επιβλέπων), Λάππας Διονύσιος Αναπλ. Καθηγ., Μπαρμπάτης Γεράσιμος Επικ. Καθηγ.
Original Title:
Ελλειπτικά συστήματα μεταβολικής μορφής με μη-κυρτές μη-γραμμικότητες
Summary:
We consider the elliptic system for maps ,
(i) for n = 2, W: a C3 triple well potential with three global minima a1, a2,
a3;
(ii) for n = 3, W: a C3 quadruple well potential with four global minima a1, a2
, a3, a4.
Under the assumption that u() is a solution partitioning space as a triple
junction in R2 or as a quadruple junction in R3 (motivated by the relationship
with minimal complexes) we establish Young’s law. This theorem can be
interpreted as a rigidity result which in particular implies that the symmetry
of the potential W imposes symmetry on the solution.
Keywords:
Calculus of Variations, Plateau Angle Conditions, Non-Linear Elliptic System
File:
File access is restricted.
document.pdf
467 KB
File access is restricted.
