International mathematical journal of analysis and its applications
CiteScore 2018: 0.72
SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530
Mathematical Citation Quotient (MCQ) 2018: 0.36
We study surfaces of prescribed mean curvature in R3 with part of their boundaries lying on a support manifold without boundary. We prove C1,μ-regularity of such a surface, whenever the support manifold is of class C2 and the surface itself is a continuous, stationary point of the associated energy functional; consequently, minimizers of that functional are included. In addition, asymptotic expansions near boundary branch points are provided. Our results improve previous work of Hildebrandt and Jäger [HJ] and Hardt [Ha], and generalize corresponding theorems on minimal surfaces. The main difficulty arises from the fact that stationary surfaces with prescribed mean curvature do not have to meet the support manifold perpendicularly, in contrast to minimal surfaces which are stationary points of Dirichlet´s functional.
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