On the Dirichlet problem for prescribed mean curvature equation over general domains

Details On the Dirichlet problem for prescribed mean curvature equation over general domains On the Dirichlet problem for prescribed mean curvature equation over general domains

2007-12-06

arxiv.org/abs/0712.0966v1

Mathematics

Differential Geometry

Scientific paper

We study and solve the Dirichlet problem for graphs of prescribed mean curvature in $\mathbb R^{n+1}$ over general domains $\Omega$ 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.

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