Surfaces of prescribed mean curvature in a cone

We show existence of surfaces of prescribed mean curvature in central projection for such values of the mean curvature for which estimates for the corresponding Euler–Lagrange equations are generally not known. This is achieved by extending the variational problem to the space B V ( Ω ) , where grap...

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Bibliographic Details
Published in:Archiv der Mathematik 2016-10, Vol.107 (4), p.429-444
Main Authors: Bemelmans, Josef, Habermann, Jens
Format: Article
Language:English
Subjects:
Curvature
Dirichlet problem
Euler-Lagrange equation
Mathematics
Mathematics and Statistics
Variational methods
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Summary:We show existence of surfaces of prescribed mean curvature in central projection for such values of the mean curvature for which estimates for the corresponding Euler–Lagrange equations are generally not known. This is achieved by extending the variational problem to the space B V ( Ω ) , where graphs in a cone must satisfy a side condition, and using variational methods. Moreover, we give an example of a solution in B V ( Ω ) which does not solve the Dirichlet problem for the Euler-Lagrange equation.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-016-0940-0