# The asymptotic behaviour of surfaces with prescribed mean curvature near meeting points of fixed and free boundaries

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2007)

- Volume: 6, Issue: 4, page 529-559
- ISSN: 0391-173X

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topMüller, Frank. "The asymptotic behaviour of surfaces with prescribed mean curvature near meeting points of fixed and free boundaries." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 6.4 (2007): 529-559. <http://eudml.org/doc/272297>.

@article{Müller2007,

abstract = {We study the shape of stationary surfaces with prescribed mean curvature in the Euclidean 3-space near boundary points where Plateau boundaries meet free boundaries. In deriving asymptotic expansions at such points, we generalize known results about minimal surfaces due to G. Dziuk. The main difficulties arise from the fact that, contrary to minimal surfaces, surfaces with prescribed mean curvature do not meet the support manifold perpendicularly along their free boundary, in general.},

author = {Müller, Frank},

journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},

keywords = {partially free boundary alue problem; Jordan arc; stationary surfaces; prescribed mean curvature; partially free boundary value problem; Jordan arc},

language = {eng},

number = {4},

pages = {529-559},

publisher = {Scuola Normale Superiore, Pisa},

title = {The asymptotic behaviour of surfaces with prescribed mean curvature near meeting points of fixed and free boundaries},

url = {http://eudml.org/doc/272297},

volume = {6},

year = {2007},

}

TY - JOUR

AU - Müller, Frank

TI - The asymptotic behaviour of surfaces with prescribed mean curvature near meeting points of fixed and free boundaries

JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

PY - 2007

PB - Scuola Normale Superiore, Pisa

VL - 6

IS - 4

SP - 529

EP - 559

AB - We study the shape of stationary surfaces with prescribed mean curvature in the Euclidean 3-space near boundary points where Plateau boundaries meet free boundaries. In deriving asymptotic expansions at such points, we generalize known results about minimal surfaces due to G. Dziuk. The main difficulties arise from the fact that, contrary to minimal surfaces, surfaces with prescribed mean curvature do not meet the support manifold perpendicularly along their free boundary, in general.

LA - eng

KW - partially free boundary alue problem; Jordan arc; stationary surfaces; prescribed mean curvature; partially free boundary value problem; Jordan arc

UR - http://eudml.org/doc/272297

ER -

## References

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- [10] F. Müller, Investigations on the regularity of surfaces with prescribed mean curvature and partially free boundaries, Habilitationsschrift, BTU Cottbus (2006).
- [11] F. Müller, On the regularity of $H$-surfaces with free boundaries on a smooth support manifold, BTU Cottbus (2007), preprint. Zbl1161.53011
- [12] F. Müller, Growth estimates for the gradient of an $H$-surface near singular points of the boundary configuration, Z. Anal. Anwendungen, to appear. Zbl1167.53012MR2469718
- [13] J. C. C. Nitsche, Minimal surfaces with partially free boundary. Least area property and Hölder continuity for boundaries satisfying a chord-arc condition, Arch. Ration. Mech. Anal. 39 (1970), 131–145. Zbl0209.41602MR266068
- [14] F. Sauvigny, “Partial Differential Equations 1: Foundations and Integral Representations", Springer, Berlin Heidelberg, 2006. Zbl1198.35001MR2254749
- [15] F. Sauvigny, “Partial Differential Equations 2: Functional Analytic Methods", Springer, Berlin Heidelberg, 2006. Zbl1198.35002MR2254750

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