Τεχνικές Επίλυσης Αντίστροφων Προβλημάτων Με Βάση Τις Συναρτήσεις Φραγμένης Κύμανσης - Μαρκάκη, Βασιλική (Εθνικό Μετσόβιο Πολυτεχνείο. Σχολή Εφαρμοσμένων Μαθηματικών και Φυσικών Επιστημών, 2017)
The present work has a first part pertaining to the presentation of the fundamental and cornerstone aspects of the inverse conductivity problem: the existence, uniqueness and stability of the solution of this problem. In the sequel, the master thesis involves the development of inversion techniques concerning the solvability of typical inverse dynamic problems in Elastography. The novel concept consists in exploiting and developing analysis from the framework of bounded variation fun\-ctions ($BV$ functions), which represent accurately the discontinuous nature of the inhomogeneities under reconstruction.\