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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

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Volume 28, Issue 4


On the regularity of H-surfaces with free boundaries on a smooth support manifold

Frank Müller
Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/anly.2008.0924


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.

Keywords: surfaces with prescribed mean curvature; free boundaries; regularity

About the article

* Correspondence address: Brandenburgische Technische Universität Cottbus, Mathematisches Institut, Konrad-Zuse-Straße 1, 03044 Cottbus, Deutschland,

Published Online: 2009-09-25

Published in Print: 2008-12-01

Citation Information: Analysis International mathematical journal of analysis and its applications, Volume 28, Issue 4, Pages 401–419, ISSN (Print) 0174-4747, DOI: https://doi.org/10.1524/anly.2008.0924.

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Frank Müller
Advances in Calculus of Variations, 2008, Volume 1, Number 4

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