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.
- Lehrende/r: Caterina Ida Zeppieri