Surfaces of prescribed mean curvature in a cone

被引：1
|
作者：
Bemelmans, Josef [1 ]
Habermann, Jens [2 ]
机构：
[1] Rhein Westfal TH Aachen, Inst Math, Templergraben 55, D-52062 Aachen, Germany
[2] Univ Erlangen Nurnberg, Dept Math, Cauerstr 11, D-91058 Erlangen, Germany
来源：
ARCHIV DER MATHEMATIK | 2016年 / 107卷 / 04期
关键词：
Graphs on prescribed mean curvature; Variational methods in BV; CENTRAL PROJECTION; HYPERSURFACES;
D O I：
10.1007/s00013-016-0940-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 BV(Omega), where graphs in a cone must satisfy a side condition, and using variational methods. Moreover, we give an example of a solution in BV(Omega) which does not solve the Dirichlet problem for the Euler-Lagrange equation.
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页码：429 / 444
页数：16
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