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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