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

Frank Müller

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

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

Abstract

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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.

How to cite

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Müller, 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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