@ARTICLE{Cl02, author = {Clarenz, U.}, title = {Enclosure Theorems for Extremals of Elliptic Parametric Functionals}, journal = {Calculus of Variations}, year = {2002}, volume = {15}, pages = {313--324}, abstract = {In this paper we study parametric functionals. First we introduce a generalized mean curvature (so called \em $F$-mean curvature\em ). This enables us to describe extremals of parametric funcionals as surfaces of prescribed $F$-mean curvature. Furthermore we give a differential equation for arbitrary immersions generalizing $\Delta X = HN$ and apply this equation to surfaces of vanishing and prescribed $F$-mean curvature. Especially we prove non-existence results for such surfaces generalizing Theorems by Hildebrandt and Dierkes.}, pdf = {http://numod.ins.uni-bonn.de/research/papers/public/Cl02.pdf} }