On the Dirichlet problem for prescribed mean curvature equation over general domains
Differential Geometry
2007-12-07 v1 Analysis of PDEs
Abstract
We study and solve the Dirichlet problem for graphs of prescribed mean curvature in over general domains without requiring a mean convexity assumption. By using pieces of nodoids as barriers we first give sufficient conditions for the solvability in case of zero boundary values. Applying a result by Schulz and Williams we can then also solve the Dirichlet problem for boundary values satisfying a Lipschitz condition.
Cite
@article{arxiv.0712.0966,
title = {On the Dirichlet problem for prescribed mean curvature equation over general domains},
author = {Matthias Bergner},
journal= {arXiv preprint arXiv:0712.0966},
year = {2007}
}