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

2007/12/06 by Matthias Bergner, Bergner, Matthias
Mathematics · #53A10 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:53A10

paper · pdf · doi:10.48550/arxiv.0712.0966

arxiv created 2007/12/06 · arxiv updated 2009/12/01

Abstract

We study and solve the Dirichlet problem for graphs of prescribed mean curvature in \mathbb Rⁿ⁺¹ over general domains Ω 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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