Kurs im HIS-LSF

Abstract

In this course we introduce the notion of functions of bounded variation (in short BV-functions) which are those functions whose distributional derivative is a Radon measure of bounded total variation. This is essentially the weakest sense in which a function can be differentiable, via measure theory.
One of the most remarkable feature of the theory of BV-functions is its deep connection with other fields of analysis such as geometric measure theory, functional analysis, and the calculus of variations. Indeed in the last decades the space of BV-functions turned out to be the natural setting to study a wide variety of problems ranging from minimal surfaces and geometrical inequalities to variational problems involving discontinuity hypersurfaces (typical examples come  from materials science and computer vision).

This course will be divided into two main parts. The first part will be devoted to develop the general theory of BV-functions while in the second part some relevant applications will be presented.