Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Author:
Κατζουράκης Νικόλαος
Dissertation committee:
Αλικάκος Νικόλαος Καθηγ.(Επιβλέπων), Στρατής Ιωάννης Καθηγ., Δούγαλης Βασίλειος Καθηγ.
Original Title:
Μη γραμμικά συστήματα ελλειπτικών περικών διαφορικών εξισώσεων
Summary:
In this dissertation we consider nonlinear eliptic systems and calculus of
variations. The thesis consists of six chapters. In the first we prove
existence of solution to a system of heteroclinic travelling waves for the
gradient Diffusion system. In the second we prove a maximum principle for
approximate vectorial minimizers of nonconvex functionals of tyhe calculus of
variations. In the third we derive the aronsson
system for regular absolute minimizers of supremal functionals. In the forth
we. Introduce a systematic theory of nondifferentiable solutions which extends
viscosity solutions to the full vector case of systems. In the fifth we
construct singular viscosity solutions of the aronsson equation and in the
sixth we construct a highly singular continuous function which furnishes
regularity counterexamples.
Keywords:
Nonlinear Systems, Calculus of variations, Aronsson equation, Viscosity solutions
Number of references:
240
