arXiv subjects

Matthias Bergner

Publications and source records attributed to Matthias Bergner.

4 recordsLinked to original sources

arXiv2007

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

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

math.DG↗

arXiv2007

A Uniqueness and Periodicity Result for Solutions of Elliptic Equations in Unbounded Domains

We proof a uniqueness and periodicity theorem for bounded solutions of uniformly elliptic equations in certain unbounded domains.

math.AP↗

arXiv2007

On Surfaces of Prescribed Weighted Mean Curvature

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.

math.DG↗

arXiv2005

On two-dimensional immersions of prescribed mean curvature in R^n

We consider two-dimensional immersions of disc-type in R^n. We focus well known classical concepts and study the nonlinear elliptic systems of such mappings. Using an Osserman-type condition we give a priori-estimates of the principle curvatures for certain graphs in R^4 with prescribed mean curvature.

math.DG↗