%0 Journal Article
%T On Surfaces of Prescribed Weighted Mean Curvature
%A Matthias Bergner
%A Jens Dittrich
%J Mathematics
%D 2007
%I arXiv
%X Utilizing a weight matrix we study surfaces of prescribed weighted mean curvature which yield a natural generalisation to critical points of anisotropic surface energies. We first derive a differential equation for the normal of immersions with prescribed weighted mean curvature, generalising a result of Clarenz and von der Mosel. Next we study graphs of prescribed weighted mean curvature, for which a quasilinear elliptic equation is proved. Using this equation, we can show height and boundary gradient estimates. Finally, we solve the Dirichlet problem for graphs of prescribed weighted mean curvature.
%U http://arxiv.org/abs/0711.2406v1