After successful completion of the course, students are able to:

-know the basic properties of functions of bounded variation and be able to apply them

-master the basics of the theory of sets of finite perimeter

-understand applications of the theory of BV functions in variational problems in imaging and materials science

Functions of bounded variation play a pivotal role in several variational problems, such as image reconstruction, modeling of fracture mechanics, and study of graphs with minimal area. This is an introductory course to the theory of functions of bounded variation. Topics will include: Radon measures, basic properties of BV functions, sets of finite perimeter, coarea formulas, as well as applications of the theory of BV functions to phase transitions and to the study of the Mumford-Shah functional.

Presentation of the course material using Zoom

Oral