Seminar Scientific Computing (Michael Bildhauer)

We consider variational problems with linear growth conditions and the related Euler equations
in the case of the existence of smooth solutions.
We are mainly interested in the generalization of classical theorems which are well known in the
minimal surface case.
In particular we discuss Liouville- and Bernstein-type results as well as an extension of a theorem
of Bers and Finn and some geometric aspects of so-called g-surfaces.
As a main ingredient a new variant of Caccioppoli’s inequality is discussed at the end of our talk.