Surfaces of prescribed mean curvature in a cone - Bemelmans, Josef; Habermann, Jens (Archiv der Mathematik, 2016)
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(Ω) , where graphs in a cone must satisfy a side condition, and using variational methods. Moreover, we give an example of a solution in BV(Ω) which does not solve the Dirichlet problem for the Euler-Lagrange equation.
UnivIS-Import:2017-01-09:Pub.2016.nat.dma.zentr.surfac
Keywords: 49J40; 49Q20; 53A10