Download or read book An Introduction to Functions of Bounded Variation, Sets of Finite Perimeter and Some Applications to Geometric Variational Problems written by Ke Liang Xiao and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In this thesis, we explore how the theory of functions of bounded variation (BV) establishes an appropriate and versatile framework in the study of geometric variational problems. We begin with a presentation of some fundamental results on BV functions that will allow us to link them to Radon measures. In the special case of characteristic functions with bounded variation, we present structural results on sets of finite perimeter, including a generalization of the Gauss-Green Theorem. This machinery will allow us to assign a notion of perimeter to any set of finite Lebesgue measure, hence allowing non- smooth competitors to be considered in minimization problems involving the surface area. We will then address Plateau's problem and the first variation of the area functional. Finally, we will present the ideas of Steiner symmetrization to provide a proof of the Isoperimetric inequality"--