TITLE

# Hï¿½lder continuity of surfaces with bounded mean curvature at corners where Plateau boundaries meet free boundaries

AUTHOR(S)
M�ller, Frank
PUB. DATE
November 2005
SOURCE
Calculus of Variations & Partial Differential Equations;Nov2005, Vol. 24 Issue 3, p283
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
Let $$P={\rm \Gamma}\cap{\cal S}$$ be the point of non-tangential intersection of a closed Jordan arc $${\rm \Gamma} \subset {\mathbb R}^{3}$$ and an embedded, regular support surface $${\cal S} \subset {\mathbb R}^{3}$$. Let $${\bf x}:B \to {\mathbb R}^{3}$$ be a conformally parametrized solution of $$|{\rm \Delta}{\bf x}|\le a|\nabla {\bf x}|^{2}$$with partially free boundaries $$\{{\rm \Gamma},{\cal S}\}$$. It is proved, that $${\bf x}$$ is Hï¿½lder continuous up to $$w_{0}\in \partial B$$ with $${\bf x}(w_{0})=P$$, whenever $${\bf x}$$ meets $${\cal S}$$ orthogonally along its free trace. This provides a regularity result for stationary minimal surfaces and is applicable also to surfaces of prescribed bounded mean curvature.
ACCESSION #
18455994

## Related Articles

• Free energy of the spherical mean field model. Talagrand, Michel // Probability Theory & Related Fields;Mar2006, Vol. 134 Issue 3, p339

We compute at any temperature the free energy of the multi p-spin spherical model when only terms for p even are considered.

• Crossover Critical Behavior in the Three-Dimensional Ising Model. Kim, Young C.; Anisimov, Mikhail A.; Sengers, Jan V.; Luijten, Erik // Journal of Statistical Physics;Mar2003, Vol. 110 Issue 3-6, p591

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction...

• Relativistic Description of Exotic Nuclei and Nuclear Matter at Extreme Conditions. Meng, J.; Ban, S. F.; Li, J.; Long, W. H.; Lü, H. F.; Zhang, S. Q.; Zhang, W.; Zhou, S.-G. // Physics of Atomic Nuclei;Sep2004, Vol. 67 Issue 9, p1619

Recent works on the relativistic description of exotic nuclei and nuclear matter at extreme conditions are reviewed. New parameter sets for the Lagrangian density in the relativistic mean field (RMF) theory, PK1, PK1r, and PKDD are proposed with the center-of-mass correction included in a...

• Theoretical simulation for identical bands. Chen, Y. J.; Chen, Y.S.; Shen, C. W.; Gao, Z. C.; Zhu, S. J.; Tu, Y. // European Physical Journal A -- Hadrons & Nuclei;May2005, Vol. 24 Issue 2, p185

The frequency of occurrence of identical bands in superdeformed and normal-deformed nuclei is studied by carrying out a statistical analysis of a large number of rotational bands, which are generated with the reflection asymmetric shell model. The frequency of occurrence and the behaviors of...

• Hyperspherical coordinates applied to two-component boson systems. Sogo, T.; Sørensen, O.; Jensen, A. S.; Fedorov, D. V. // AIP Conference Proceedings;2005, Vol. 768 Issue 1, p442

Structure and stability for two-component boson systems are studied by use of the hyperadii of the two systems and the distance between their centers. Sufficiently strong repulsion between different bosons form stable structures at a finite distance between the centers. This repulsion also leads...

• Segmental relaxation in semicrystalline polymers: A mean-field model for the distribution of relaxation times in confined regimes. Pieruccini, M.; Ezquerra, T.A. // European Physical Journal E -- Soft Matter;Jun2009, Vol. 29 Issue 2, p163

The effect of confinement in the segmental relaxation of polymers is considered. On the basis of a thermodynamic model we discuss the emerging relevance of the fast degrees of freedom in stimulating the much slower segmental relaxation, as an effect of the constraints at the walls of the...

• More is the Same; Phase Transitions and Mean Field Theories. Kadanoff, Leo P. // Journal of Statistical Physics;Dec2009, Vol. 137 Issue 5/6, p777

This paper is the first in a series that will look at the theory of phase transitions from the perspectives of physics and the philosophy of science. The series will consider a group of related concepts derived from condensed matter and statistical physics. The key technical ideas go under the...

• The Time Evolution of Fluctuation Algebra in Mean Field Theories. Narnhofer, Heide // Foundations of Physics Letters;Jun2004, Vol. 17 Issue 3, p235

Fluctuation algebra is defined for equilibrium states of mean field theories. The time evolution is calculated; and, in contrast to interactions with finite range, the fluctuation algebra is not in a KMS state with respect to this time evolution though the underlying quasilocal state. If the...

• Free-Boundary Regularity for a Problem Arising in Superconductivity. Caffarelli, Luis; Salazar, Jorge; Shahgholian, Henrik // Archive for Rational Mechanics & Analysis;Jan2004, Vol. 171 Issue 1, p115

This paper concerns regularity properties of the mean-field theory of superconductivity. The problem is reminiscent of the one studied earlier by L.A. Caffarelli, L. Karp and H. Shahgholian in connection with potential theory. The difficulty introduced in this paper is the existence of several...

Share