Existence and Regularity Theory for Functionals of Linear Growth

In this talk I give an overview of new existence and regularity results for functionals of linear growth which either depend on the full gradient (leading to the space BV) or specific combinations of derivatives (leading to the spaces BVA). Since in general there are no Korn--type inequalities available for p=1 - which is usually referred to as Ornstein-type Non-inequalities - the latter spaces are genuinely strictly larger than BV and encompass, e.g., the space BD of functions of bounded deformation which plays an important role in perfect plasticity.